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	PlanetMath: Weil conjectures
		Conjectures made by Weil on the form of the zeta function of a variety over a finite field.
		Specifically he thought it should be rational, it should split into polynomial parts with integral coefficients, with roots of a certain magnitude, and of degree = Betti number.
		This is version 2 of Weil conjectures, born on 2006-03-03, modified 2006-03-03.
	planetmath.org /encyclopedia/WeilConjectures.html (82 words)

	Weil conjectures (Site not responding. Last check: 2007-10-19)
		In mathematics, the Weil conjectures, which had become theorems by 1975, were some highly-influential proposals from the late 1940s by Andre Weil on the generating functions (known as local zeta-functions) derived from counting the number of points on algebraic varieties over finite fields.
		Given that finite fields are discrete in nature and topology speaks only about the continuous, the detailed formulation of Weil (based on working out some examples) was striking in the way that it suggested that geometry over finite fields should fit into well-known patterns relating to Betti numbers, the Lefschetz fixed-point theorem and so on.
		The conjectures of Weil have therefore taken their place within the general theory (of L-functions, in the broad sense).
	www.1-free-software.com /en/wikipedia/w/we/weil_conjectures.html (399 words)

	Andre Weil: 1906-1998
		The legendary Weil had retired from the Institute seven years earlier, at the age of 70, but he continued to live on the grounds and I knew that he was a frequent presence at both seminars and social events.
		Weil was able to prove that the geometric structure of a curve conveys---in ways that are highly subtle and not at all obvious---information about the arithmetic of the associated equation.
		Weil was teaching at Strasbourg and engaged in endless discussions with his colleague Henri Cartan about the "right'' way to present various mathematical concepts to students.
	www.landsburg.com /weil.htm (2614 words)

	Weil conjectures - Wikipedia, the free encyclopedia
		In mathematics, the Weil conjectures, which had become theorems by 1974, were some highly-influential proposals from the late 1940s by André Weil on the generating functions (known as local zeta-functions) derived from counting the number of points on algebraic varieties over finite fields.
		The main burden was that such zeta-functions should be rational functions, should satisfy a form of functional equation, and should have their zeroes in restricted places.
		Their interest was obvious enough from within number theory: they implied the existence of machinery that would provide upper bounds for exponential sums, a basic concern in analytic number theory.
	www.wikipedia.org /wiki/Weil_conjecture (417 words)

	Weil
		Weil was arrested in Finland and when letters in Russian were found in his room (they were actually from Pontryagin describing mathematical research) things looked pretty fl.
		Weil was certainly in great danger at this time, partly because he was Jewish, partly because he had a sister Simone Weil who was a mystic philosopher and a leading figure in the French Resistance.
		The dangers of his predicament made Weil decide that being in the army was a better bet and he was able to argue successfully for his release on the condition that indeed he did join the army.
	www-groups.dcs.st-and.ac.uk /~history/Mathematicians/Weil.html (1300 words)

	Kids.net.au - Encyclopedia André Weil - (Site not responding. Last check: 2007-10-19)
		André Weil (May 6, 1906 - August 6, 1998) was one of the great mathematicians of the 20th century, a founding member of the influential Bourbaki group.
		A famous anecdote was confirmed in his autobiography: after having been arrested under suspicion of espionage in Finland, he was saved from being shot only by the intervention of Rolf Nevanlinna.
		After the war, Weil went to the United States where he taught at the University of Chicago before settling at the Institute for Advanced Study at Princeton University.
	www.kids.net.au /encyclopedia-wiki/an/Andre_Weil (178 words)

	[No title]
		Dwork's conjecture can be viewed as the starting point of a truly p-adic extension of the Weil conjectures from a single variety over a finite field to a family of varieties over a finite field.
		Conjecturally, this category should be the p-adic analogue of lisse l-adic sheaves and thus the Weil conjectures are expected to extend to this category of overconvergent F-crystals.
		It is conjectured that an irreducible overconvergent unit root F-crystal whose determinant is a character of finite order is the "p-part" of a compatible l-adic system, a p-adic "analogue" of Delinge's l-adic conjecture in Weil II.
	www.math.uci.edu /~dwan/letter (4948 words)

	Encyclopedia: AndrÃ© Weil (Site not responding. Last check: 2007-10-19)
		University of Chicago before settling at the The Institute for Advanced Study is a private institution in Princeton Township, New Jersey, designed to foster pure cutting_edge research by scientists in a variety of fields without the complications of teaching or funding, or the agendas of sponsorship.
		André Weil should not be confused with Andrew John Wiles (born April 11, 1953) is a British mathematician living in the United States.
		See also: In mathematics, the Weil pairing is a construction of roots of unity by means of functions on an elliptic curve E, in such a way as to constitute a pairing (bilinear form, though with multiplicative notation) on the torsion subgroup of E. The name is for André Weil, who gave...
	www.nationmaster.com /encyclopedia/Andr%E9-Weil (988 words)

	André Weil, Who Reshaped Mathematics, Is Dead at 92 (Site not responding. Last check: 2007-10-19)
		In 1994, Dr. Weil (pronounced VAY) won the equivalent of the Nobel Prize, which is not awarded in mathematics, when he received the Kyoto Prize in Basic Science from the Inamori Foundation of Kyoto, Japan.
		Weil was born in 1906 in Paris, became devoted to mathematics in his early teens and received his doctorate from the University of Paris in 1928.
		Weil was one of the founders of the influential Bourbaki, a group of French mathematicians who rebelled against the French establishment and whose original writings from the 1930's unified all of mathematical knowledge for the first time.
	www.ishipress.com /weil-obi.htm (779 words)

	Weil conjectures -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-19)
		The main burden was that such zeta-functions should be (Click link for more info and facts about rational function) rational functions, should satisfy a form of (Click link for more info and facts about functional equation) functional equation, and should have their zeroes in restricted places.
		The rationality part of the conjectures was proved first, by (Click link for more info and facts about Bernard Dwork) Bernard Dwork, using (Click link for more info and facts about p-adic) p-adic methods.
		The conjectures of Weil have therefore taken their place within the general theory (of (Click link for more info and facts about L-function) L-functions, in the broad sense).
	www.absoluteastronomy.com /encyclopedia/W/We/Weil_conjectures.htm (508 words)

	Weil Pump Company (Site not responding. Last check: 2007-10-19)
		Weil excelled from a young age, proficient at Ancient Greek at 12.
		These Weil conjectures were made by Weil around 1949.
		The Taniyama-Shimura conjecture was made about the time of the conference in Nikko, in 1954.
	www.wwwtln.com /finance/202/weil-pump-company.html (999 words)

	Deligne (Site not responding. Last check: 2007-10-19)
		Weil's work on polynomial equations led to questions on what properties of a geometric object can be determined purely algebraically.
		A solution of the three Weil conjectures was given by Deligne in 1974.
		These conjectures were both exceptionally hard to settle (the best specialists, including A Grothendieck, had worked on them) and most interesting in view of the far-reaching consequences of their solution.
	www-groups.dcs.st-and.ac.uk /~history/Mathematicians/Deligne.html (998 words)

	Times obituary (Site not responding. Last check: 2007-10-19)
		One of the most respected mathematicians of the second half of this century, Andre Weil is best known for two things: his fundamental discoveries in number theory, and his membership of the secretive group known as Bourbaki, which redefined the foundations of modern pure mathematics.
		Weil made his way to Italy, and then to Gottingen, hub of German mathematics and home of the legendary David Hilbert.
		Andre Weil will be remembered for his fundamental work on the frontiers of mathematics, and for his carefully cultivated image as a cantankerous character -- belied by his dry sense of humour.
	www.aam314.vzz.net /Weil.html (851 words)

	Science Fair Projects - Motivic cohomology
		At that time, it was conceived as a theory constructed on the basis of the so-called standard conjectures on algebraic cycles, in algebraic geometry.
		It had a basis in category theory for drawing consequences from those conjectures; Grothendieck and Bombieri showed the depth of this approach by deriving a conditional proof of the Weil conjectures by this route.
		Serre, for example, preferred to work more concretely with a system of compatible l-adic representations, which at least conjecturally should be as good as having a motive, but instead listed the data obtainable from a motive by means of its 'realisations' in the etale cohomology theories with l-adic coefficients, as l varied over prime numbers.
	www.all-science-fair-projects.com /science_fair_projects_encyclopedia/Motivic_cohomology (427 words)

	Weil (Site not responding. Last check: 2007-10-19)
		In fact Weil's work in this area was basic to work by mathematicians such as Yau who was awarded a Fields Medal in 1982 for work in three dimensional algebraic geometry which has major applications to quantum field theory.
		One of Weil's major achievements was his proof of the Riemann hypothesis for the congruence zeta functions of algebraic function fields.
		These Weil conjectures, as they came to be called, grew out of his deep insight into the topology of algebraic varieties and provided guiding principles for subsequent developments in the field.
	www.bg-rams.ac.at /intranet/Physik/history/Weil.html (955 words)

	Weil conjectures: Definition and Links by Encyclopedian.com - All about Weil conjectures (Site not responding. Last check: 2007-10-19)
		The Weil conjectures, which had become theorems by 1975, were some highly-influential proposals by Andre Weil on the generating functions (known as local zeta-functions[?]) derived from counting the number of points on algebraic varieties over finite fields.
		The rest awaited the construction of etale cohomology[?], a theory whose very definition lies quite deep.
		Since etale cohomology has had many other applications, this development exemplifies the relationship between conjectures (based on examples, guesswork and intuition), theory-building, problem-solving, and spin-offs, even in the most abstract parts of pure mathematics.
	www.encyclopedian.com /we/Weil-conjecture.html (411 words)

	Langweilige Mitteilungen
		2) kamen zu spät zur podiumsdiskussion mit sigrid löffler und gingen nach fünfzehn minuten wieder, weil ich befürchtete, mich vor trunkenheit in der theaterloge übergeben zu müssen.
		habe für heute mit dem lernen aufgehört, weil ich inzwischen eine chevy-chase-strophe erkenne, wenn ich eine lese.
		chevy chase ist übrigens nebenbei ein amerikanischer komödiant, weil man ja nicht 24/7 ballade sein kann (vergleiche dazu auch tropen, welche nebenbei eine klimazone sind, weil man nicht 24/7 rhetorische stilfiguren sein kann).
	www.fairfox.net (2806 words)

	André Weil -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-19)
		André Weil (May 6, 1906 - August 6, 1998) was one of the great (A person skilled in mathematics) mathematicians of the (Click link for more info and facts about 20th century) 20th century, a founding member of the influential (Click link for more info and facts about Bourbaki group) Bourbaki group.
		He was brother of the (A specialist in philosophy) philosopher (French philosopher (1909-1943)) Simone Weil.
		André Weil should not be confused with (Click link for more info and facts about Andrew Wiles) Andrew Wiles, another famous mathematician who, like Weil, has done important work in (Click link for more info and facts about elliptic curve) elliptic curves; the similarity of their names is a coincidence.
	www.absoluteastronomy.com /encyclopedia/A/An/Andr%E9_Weil.htm (246 words)

	Amazon.de: Bücher: Weil Conjectures, Perverse Sheaves and l'adic Fourier Transform (Site not responding. Last check: 2007-10-19)
		Amazon.de: Bücher: Weil Conjectures, Perverse Sheaves and l'adic Fourier Transform
		In this book the authors describe the important generalization of the original Weil conjectures, as given by P. Deligne in his fundamental paper "La conjecture de Weil II".
		Zum Seitenanfang : Weil Conjectures, Perverse Sheaves and l'adic Fourier Transform
	www.amazon.de /exec/obidos/ASIN/3540414576/xmlbibliothek (457 words)

	Jean-Pierre_Serre (Site not responding. Last check: 2007-10-19)
		Jean-Pierre Serre (born September 15, 1926) is one of the leading mathematicians of the twentieth century, active in algebraic geometry, number theory and topology.
		While Serre subsequently moved field — at this point he apparently thought that homotopy theory where he had started was already over-technical — Weyl's perception that the central place of classical analysis had been challenged by abstract algebra has subsequently been justified, as has his assessment of Serre's place in this change.
		Amongst his most original contributions were: the concept of algebraic K-theory; the Galois representation theory for l-adic cohomology and the conceptions that these representations were 'large'; and the Serre conjecture on mod p representations that made Fermat's last theorem a connected part of mainstream arithmetic geometry.
	www.apawn.com /search.php?title=Jean-Pierre_Serre (526 words)

	MAT1191HF - Topics in Algebraic Geometry: Grothendieck groups, Chow motives. (Site not responding. Last check: 2007-10-19)
		The theory of motives was concieved by A. Grothendieck in the 60's with the purpose to study (i.e.
		Weil conjectures are consequences of 2 stronger statements of topological nature: the Standard Conjectures.
		I will explain and comment the statements of these conjectures and then, head to the defintion of a pure Chow motive.
	www.math.toronto.edu /kc/1191hf.html (243 words)

	Weil Conjectures, Perverse Sheaves and l'adic Fourier Transform (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. ...
		Weil Conjectures, Perverse Sheaves and l'adic Fourier Transform (Ergebnisse der Mathematik und ihrer Grenzgebiete.
		Synopsis In this volume the authors describe the important generalization of the original Weil conjectures, as given by P. Deligne in his fundamental paper "La conjecture de Weil II".
		Kategorientheorie > Weil Conjectures, Perverse Sheaves and l'adic Fourier Transform (Ergebnisse der Mathematik und ihrer Grenzgebiete.
	www.uni-protokolle.de /buecher/isbn/3540414576 (314 words)

	Encyclopedia: AndrÃ© Weil (Site not responding. Last check: 2007-10-19)
		Among his accomplishments were the so_called In mathematics, the Weil conjectures, which had become theorems by 1975, were some highly_influential proposals from the late 1940s by Andre Weil on the generating functions (known as local zeta_functions) derived from counting the number of points on algebraic varieties over finite fields.
		Weil conjectures (later proved by Bernard Dwork, Alexander Grothendieck (born March 28, 1928, Berlin) is one of the greatest mathematicians of the 20th century, with major contributions to algebraic geometry, homological algebra, and functional analysis.
		function fields, laying proper foundations for algebraic geometry, and discovery that the so_called Weil representation, previously introduced in Fig.
	www.nationmaster.com /encyclopedia/Andr%C3%A9-Weil (988 words)

	Conjeturas de Weil (Site not responding. Last check: 2007-10-19)
		En matemáticas, las conjeturas de Weil, que tenían teoremas convertidos antes de 1975, eran algunas ofertas alto-influyentes a partir de los últimos años 40 de Andre Weil en las funciones que generaban (conocidas como zeta-funciones locales) derivadas de contar el número de puntos en campos finitos del excedente algebraico de las variedades.
		Weil mismo, es dicha, nunca realmente probado probar las conjeturas.
		Las conjeturas de Weil por lo tanto han tomado su lugar dentro de la teoría general (de L-funciones, en el amplio sentido).
	www.yotor.net /wiki/es/co/Conjeturas%20de%20Weil.htm (398 words)

	U of R Number Theory seminar (Site not responding. Last check: 2007-10-19)
		This talk is a sequel to the SUMS talk of February 19 in which I explained the subject of the Weil conjectures.
		This information is encoded in the zeta function of X, which is what the Weil conjectures are about.
		Weil's program to prove his conjectures was to find an analog to this topological method in algebraic geometry in characteristic p.
	www.math.rochester.edu /research/algebra_and_number_theory/2.26.03.html (165 words)

	Science Fair Projects - Étale cohomology
		In mathematics, the étale cohomology theory of algebraic geometry is a refined construction of homological algebra, introduced in order to attack the Weil conjectures.
		This theory is an example of a Weil cohomology theory in algebraic geometry, and as such it continues to play an important role in the more general theory of motives.
		The formal definition of étale cohomology is as the derived functor of the functor of sections,
	www.all-science-fair-projects.com /science_fair_projects_encyclopedia/%C9tale_cohomology (1063 words)

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