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Topic: Grothendieck

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	Alexander Grothendieck - Wikipedia, the free encyclopedia
		Alexander Grothendieck (born March 28, 1928 in Berlin, Germany) is one of the most important mathematicians of the 20th century.
		The Grothendieck-Riemann-Roch theorem was announced by Grothendieck at the initial Mathematische Arbeitstagung in Bonn, in 1957.
		Perhaps Grothendieck's deepest single accomplishment is the invention of the étale and l-adic cohomology theories, which explain an observation of André Weil's, that there is a deep connection between the topological characteristics of a variety and its diophantine (number theoretic) properties.
	en.wikipedia.org /wiki/Alexander_Grothendieck (1972 words)

	Grothendieck biography
		It is no exaggeration to speak of Grothendieck's years 1959-70 at the IHES as a 'Golden Age', during which a whole new school of mathematics flourished under Grothendieck's charismatic leadership.
		In looking back at this period, one marvels at the generosity with which Grothendieck shared his ideas with colleagues and students, the energy he and his collaborators devoted to meticulous redaction, the excitement with which they set out to explore a new land.
		Grothendieck was always strongly pacifist in his views and campaigned against the military built-up of the 1960s.
	www-history.mcs.st-andrews.ac.uk /Biographies/Grothendieck.html (535 words)

	The Spectator.co.uk
		In the first place, the luminous brilliance of Grothendieck’s mathematical achievement — his 1966 Fields Medal, the Nobel Prize of maths, is an indicator — is matched only by the near impossibility of explaining it to anyone without a background in pure maths.
		Grothendieck doesn’t write popularising books like Stephen Hawking; he doesn’t tour American universities lecturing undergraduates; and he doesn’t, any more, publish his researches and discoveries in mathematical journals.
		Grothendieck’s father was an anarchist who died in Auschwitz; Alexandre, along with his German mother Hanka, was interned in France during the war as an ‘undesirable’.
	www.lewrockwell.com /spectator/spec262.html (1224 words)

	Letter from Grothendieck \| The n-Category Café
		Alexander Grothendieck was the most visionary and radical mathematician in the second half of the 20th century - at least before he left his home and disappeared one fine day in 1991.
		Leila Schneps, an expert on Grothendieck’s theory of dessins d’enfants and a founding member of the Grothendieck Circle, was one of the last mathematicians to meet Grothendieck and correspond with him.
		It is sad tht while Grothendieck was asking the right question: “what is the metre” and rightly saying that the convention c = 300,000,000 m/s would have been simpler the standard reaction to his query was to see there the clear symptom of a deranged mind.
	golem.ph.utexas.edu /category/2006/08/letter_from_grothendieck.html (1794 words)

	Math
		Grothendieck's own description of the main themes of his life's work, written in 1972.
		Scans of Grothendieck's prenotes for EGA 5 (171 pages)- The prenotes were given to Piotr Blass by Grothendieck many years ago.
		Crystals letter to Tate (May 1966) - A 31-page letter from Grothendieck to Tate, in which the notion of crystals was born and baptized (with a nice ``commentaire terminologique'' about the name).
	www.math.jussieu.fr /~leila/grothendieckcircle/mathtexts.php (1144 words)

	Math (Site not responding. Last check: 2007-11-03)
		The Camp de Rieucros where Grothendieck and his mother spent part of the war On November 12, 1938 the law concerning `undesirables' was passed; among others, all Germans residing in France were to be interned in special camps.
		The rising tide: Grothendieck on simplicity and generality A streaming video of a talk at MSRI by Colin McLarty on Grothendieck’s approach to mathematics.
		Alexander Grothendieck (in Italian) An overview of Grothendieck's mathematical contribution by Luca Barbieri Viale.
	www.math.jussieu.fr /~leila/grothendieckcircle/biographic.php (1182 words)

	Grothendieck topology - Wikipedia, the free encyclopedia
		In category theory, a branch of mathematics, a Grothendieck topology is a structure on a category C which makes the objects of C act like the open sets of a topological space.
		While Grothendieck topologies are most often used to define cohomology theories, they have found other applications as well, such as to John Tate's theory of rigid analytic geometry.
		Grothendieck saw that it would be possible to use Serre's idea to define a cohomology theory which he suspected would be the Weil cohomology.
	en.wikipedia.org /wiki/Grothendieck_topology (3248 words)

	PlanetMath: Grothendieck group
		The Grothendieck group construction is a functor from the category of abelian semigroups to the category of abelian groups.
		the Grothendieck group of the isomorphism classes of objects of
		This is version 6 of Grothendieck group, born on 2003-05-21, modified 2006-12-04.
	planetmath.org /encyclopedia/GrothendieckGroup.html (145 words)

	Not Even Wrong » Blog Archive » Grothendieck Biographical Article
		Evidently Winfried Scharlau is writing a biography of Grothendieck, and Jackson’s article is partially based on materials he has gathered.
		Much of this material is brought together at a website maintained by the “Grothendieck Circle”.
		Illusie was a student of Grothendieck’s, and Jackson’s article has some of his reminiscences about what that experience was like.
	www.math.columbia.edu /~woit/wordpress/?p=78 (1414 words)

	Read This: Briefly Noted, June 2004
		In a famous 1954 speech, Hermann Weyl said of Jean-Pierre Serre, "never before have I witnessed such a brilliant ascension of a star in the mathematical sky as yours." Surely Weyl would have been equally impressed that Serre's star is still burning bright some 50 years later.
		It was visibly coming to those who looked in the right place in 1954, arguably brighter than all the other celestial objects in the period 1958-1970, and then occasionally visible (but only by telescope) since.
		We earthbound mathematicians have trouble understanding Grothendieck, what with his extreme abstraction and his utter independence from examples.
	www.maa.org /reviews/brief_jun04.html (2003 words)

	Springer Online Reference Works
		A category equipped with a Grothendieck topology, that is, with a structure of "coverings" which makes it possible to define the notion of a sheaf on the category.
		The category of Abelian groups in a Grothendieck topos (equivalently, the category of sheaves of Abelian groups on a site) is a Grothendieck category, which makes it possible to define sheaf cohomology on a site; the cohomology groups
		Subsequently, they have been found useful in other contexts, notably in the construction of models for synthetic differential geometry [a3], [a4].
	eom.springer.de /s/s085660.htm (506 words)

	Grothendieck Project
		By typing the name "Grothendieck" into Internet search engines, he soon uncovered the advertising for series of articles entitled the "Quest for Grothendieck" which I'd published in the Ferment newsletter in the early 90's.
		Harvey was interested in producing a comprehensive biography of Grothendieck.
		By 11 AM I was walking through the door of the Ideal Hotel on the rue de Trois Bornes in the 11th Arrondisement.
	www.fermentmagazine.org /Grotproj.html (1800 words)

	Foreign Dispatches: Grothendieck Primes
		One striking characteristic of Grothendieck’s mode of thinking is that it seemed to rely so little on examples.
		In a mathematical conversation, someone suggested to Grothendieck that they should consider a particular prime number.
		Real, breathing, cutting edge mathematics has very little to do with the kind of tedious number-crunching that is standard fare at high-school level.
	foreigndispatches.typepad.com /dispatches/2004/12/grothendieck_pr.html (476 words)

	Quest for Alexandre Grothendieck (Site not responding. Last check: 2007-11-03)
		Although his productive research ended in 1975, many mathematicians maintain that Alexandre Grothendieck is the greatest living mathematician.
		The author organized a committee to search for him that led to his discovery, in good health and busily at work, in September, 1996.
		This committee has since become the Grothendieck Biography Project.
	www.fermentmagazine.org /Publicity/Science/quest.html (336 words)

	Logic.Grothendieck (Site not responding. Last check: 2007-11-03)
		The Grothendieck logic is defined to be the heterogeneous logic over the logic graph.
		This will be the logic over which the data structures and algorithms for specification in-the-large are built.
		Embedding of homogeneous signature morphisms as Grothendieck sig mors
	www.informatik.uni-bremen.de /~luettich/hets/Logic.Grothendieck.html (1125 words)

	Cohomology in Grothendieck Topologies and Lower Bounds in Boolean Complexity (Site not responding. Last check: 2007-11-03)
		We describe an approach to attacking such questions with cohomology, and we show that using Grothendieck topologies and other ideas from the Grothendieck school gives new hope for such an attack.
		Given two sheaves on a Grothendieck topology, their cohomological complexity is the sum of the dimensions of their Ext groups.
		We seek to model the depth complexity of Boolean functions by the cohomological complexity of sheaves on a Grothendieck topology.
	www.math.ubc.ca /~jf/pubs/web_stuff/groth1.html (231 words)

	My Favorite Mathematicians: Alexandre Grothendieck (Site not responding. Last check: 2007-11-03)
		Grothendieck revealed the importance of covering in algebra.
		The importance of his ideas for mathematics is only beginning to be felt.
		THE QUEST FOR GROTHENDIECK by Roy Lisker, Ferment Press.
	homepages.feis.herts.ac.uk /~comqcln/grothendieck.html (97 words)

	Graded associative algebras and Grothendieck Standard Conjectures
		This paper is concerned with Grothendieck's standard conjectures on algebraic cycles, introduced independently by Grothendieck and Bombieri to explain the Weil conjectures on the
		Thus, with Jannsen's theorem our result asserts that the standard conjecture of Lefschetz type follows from Grothendieck's conjecture about the equality of the numerical and homological equivalences.
		This was known before only in the presence of the standard conjecture of Hodge type.
	math.cofc.edu /smirnov/conject.html (112 words)

	The Mathematics Genealogy Project - Alexandre Grothendieck
		Click here to see the students listed in chronological order.
		According to our current on-line database, Alexandre Grothendieck has 8 students and 123 descendants.
		If you have additional information or corrections regarding this mathematician, please use the update form.
	www.genealogy.ams.org /html/id.phtml?id=31245 (78 words)

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