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# Topic: Alexander Grothendieck

###### In the News (Mon 19 Aug 19)

 Alexander Grothendieck - Wikipedia, the free encyclopedia Alexander Grothendieck (Berlin, March 28, 1928) is one of the most important mathematicians of the 20th century. 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. Alexander lived with his father, Alexander Shapiro, and his mother, Hanka Grothendieck, both of whom were socialist revolutionaries. en.wikipedia.org /wiki/Alexander_Grothendieck   (1632 words)

 Alexander Grothendieck Alexander Grothendieck, born in 1928 in Berlin, is one of the leading mathematicians of the twentieth century, with monumental contributions to functional analysis and algebraic geometry. Perhaps Grothendieck's deepest accomplishment is the invention of the etale and l-adic cohomology theories, which explain an observation of Weil's, that there is a deep connection between the topological characteristics of a variety and its diophantine (number theoretic) properties. Grothendieck's radical left-wing and pacifist politics were doubtless born of his wartime experiences. www.ebroadcast.com.au /lookup/encyclopedia/al/Alexander_Grothendieck.html   (503 words)

 Grothendieck : The Other Name Of Struggle   (Site not responding. Last check: 2007-10-21) Grothendieck, born in 1928 in Berlin, was the greatest exponent of pure mathematics during the second half of last century, a name uttered with equal reverence in the community of mathematicians as that of Einstein among physicists. Grothendieck was pacifist to the core of his heart, and it was far from a passive one. However, the political views of Grothendieck, declining to dissociate science from the socio-political aspects, was totally unacceptable and alarming to Motchane, who was in fact the representative of the capitalist state determined to keep the intelligentsia under its firm control. www.peoplesmarch.com /archives/2004/jan2k4/grothendieck.htm   (2178 words)

 Alexander Grothendieck Biography / Biography of Alexander Grothendieck World of Mathematics Biography Alexander Grothendieck has had an influence on the mathematics of the second half of the 20th century well beyond the scale of his publications. Grothendieck started off as an especially prolific contributor to each of the areas to which he turned, including functional analysis, algebraic geometry, and category theory, only to move away from mathematics later in his career. Grothendieck's early years have been difficult to reconstruct, due to his reluctance to deal in ordinary reminiscences and his distrust of biographers. www.bookrags.com /biography-alexander-grothendieck-wom   (249 words)

 Jewish Fields Medalists   (Site not responding. Last check: 2007-10-21) Grothendieck's father was a Russian Jew surnamed Shapiro and his mother a German Jewish women named Hanka Grothendieck. "Grothendieck" was not that of his mother, but rather that of a governess who cared for him in Germany between 1929 and 1939. Grothendieck's father was Jewish and was deported and murdered at Auschwitz, and Grothendieck himself was sheltered (along with several thousand other Jews) in the French Protestant village of Le Chambon-sur-Lignon in southern France. www.jinfo.org /Fields_Mathematics.html   (442 words)

 Alexander Grothendieck at opensource encyclopedia   (Site not responding. Last check: 2007-10-21) Alexander Grothendieck (born March 28 1928 in Berlin), is one of the leading mathematicians of the twentieth century, with major contributions to algebraic geometry, homological algebra, and functional analysis. Born to a Jewish father and German mother, he was a displaced person during much of his childhood due to the upheavals of World War II. Grothendieck biography project by eccentric writer/mathemetician Roy Lisker. www.wiki.tatet.com /Alexander_Grothendieck.html   (1267 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   (1099 words)

 Alexander Grothendieck Biography / Biography of Alexander Grothendieck 1950 To Present: Mathematics Biography Alexander Grothendieck is regarded by many as one of the preeminent mathematicians of the twentieth century. He is credited with establishing a new school of algebraic geometry, and his work garnered a Fields Medal in 1966 for advancement of K-theory (Grothendieck groups and rings). Born in Berlin, Grothendieck emigrated to France 1941. www.bookrags.com /biography-alexander-grothendieck-scit-07123   (210 words)

 Alexander Grothendieck   (Site not responding. Last check: 2007-10-21) Homological methods and sheaf theory had already been introduced in algebraic geometry by Leray and by Serre, but Grothendieck took them to a higher level. His work is at a higher level of abstraction than prior versions of algebraic geometries, but due to its great power his theory of schemes has become established as the best foundations for this important field. This program culminated in the proofs of the Weil conjectures by Deligne in the early 1970's after Grothendieck had withdrawn from mathematics. brandt.kurowski.net /projects/lsa/wiki/view.cgi?doc=429   (375 words)

 Topos - Psychology Central   (Site not responding. Last check: 2007-10-21) This idea was expounded by Alexander Grothendieck by introducing the notion of a topos (plural: topoi or toposes — this is a contentious topic). The main utility of this notion is in the abundance of situations in mathematics where topological intuition is very effective but an honest topological space is lacking; it is sometimes possible to find a topos formalizing the intuition. Grothendieck and Verdier: Theorie des topos et cohomologie etale des schemas (known as SGA4)" psychcentral.com /psypsych/Topos   (1205 words)

 SGA   (Site not responding. Last check: 2007-10-21) The Grothendieck Circle's goal is to "make publicly available (and in some cases translate) the material written by and about Alexandre Grothendieck, as well as to provide biographical material on Grothendieck's life and his origins." The paper From Grothendieck to Connes and Kontsevich. Excerpt: "[Grothendieck] enjoyed playing the role of a modern Socrates, and was given a suspended sentence of six months in prison and a fine of 20,000 francs. modular.fas.harvard.edu /sga   (288 words)

 Scheme mathematics - Term Explanation on IndexSuche.Com Grothendieck and Dieudonné studied the category of all schemes, and Grothendieck's student Pierre_Deligne later wrote that admitting bizarre schemes made the whole category of schemes much nicer. The term prescheme has fallen out of use, but can still be found in older books, such as Grothendieck's Éléments_de_géométrie_algébrique and Mumford's ''Red Book''. According to a basic idea of Grothendieck, conditions should be applied to a ''morphism'' of schemes. www.indexsuche.com /Scheme_(mathematics).html   (926 words)

 Cassels, J. W. S. - Geometric Galois Actions: Volume 1, Around Grothendieck's Esquisse D'un Programme Books at Real ... By Grothendieck, Alexander (Author), Schneps, Leila (Editor), Lochak, Pierre (Editor), Cassels, J. (Series Editor). It contains several articles on subjects directly related to the ideas explored in the manuscripts, including surveys of mathematics due to Grothendieck, explanations of points raised in the Esquisse, and surveys on progress in the domains described there. Grothendieck, Alexander (Author),Schneps, Leila (Editor),Lochak, Pierre (Editor),Cassels, J. (Series Editor). www.realgroovy.co.nz /books/isbn/0521596424   (522 words)

 The Ultimate Sheaf - American History Information Guide and Reference   (Site not responding. Last check: 2007-10-21) Then Alexander Grothendieck used derived functors of the global section functor, providing a more definitive solution. Grothendieck was motivated to develop a cohomology theory for sheaves that would give stronger results, and that would, in particular, allow a proof of the Weil conjectures. By precisely analyzing the properties of X needed to define sheaves, he defined the notion of a Grothendieck topology on a category (this came in a somewhat roundabout fashion — see background and genesis of topos theory). www.historymania.com /american_history/Sheaf   (2927 words)

 Chern class - ExampleProblems Alernatively, Alexander Grothendieck replaced these with a slightly smaller set of axioms: There is also an approach of Alexander Grothendieck showing that axiomatically one need only define the line bundle case. As stated above, using the Grothendieck additivity axiom for Chern classes, the first of these identities can be generalized to state that ch is a homomorphism of abelian groups from the K-theory K(X) into the rational cohomology of X. www.exampleproblems.com /wiki/index.php/Chern_class   (1793 words)

 Topos - Indopedia, the Indological knowledgebase Alexander Grothendieck generalized the concept of a sheaf. The result is the category of sheaves with respect to a Grothendieck topology - also called a Grothendieck topos. Lawvere realized the logical content of this structure, and his axioms led to the current notion. www.indopedia.org /Topos.html   (1088 words)

 Math 256AB - 2005-06 The foundations of modern algebraic geometry were laid down by Alexander Grothendieck and his collaborators in the 1960's. My intention is to base the course fairly directly on Grothendieck's treatise "Éléments de géométrie algébrique" (generally known as EGA), and perhaps parts of "Séminaire de Géometrie Algébrique" (SGA). A. Grothendieck and collaborators, Séminaire de Géométrie Algébrique, 1-7. math.berkeley.edu /~mhaiman/math256   (634 words)

 Grothendieck's problems concerning profinite completions and representations of groups, Martin R. Bridson, Fritz J. ... Grothendieck's problems concerning profinite completions and representations of groups, Martin R. Bridson, Fritz J. Grunewald In 1970 Alexander Grothendieck posed the following problem: let $\G_1$ and $\G_2$ be finitely presented, residually finite groups, and let $u:\G_1\to\G_2$ be a homomorphism such that the induced map of profinite completions $\hat u :\hat\G_1\to\hat\G_2$ is an isomorphism; does it follow that $u$ is an isomorphism? The same construction allows us to settle a second problem of Grothendieck by exhibiting finitely presented, residually finite groups $P$ that have infinite index in their Tannaka duality groups ${\rm cl}_A(P)$ for every commutative ring $A\neq 0$. projecteuclid.org /Dienst/UI/1.0/Summarize/euclid.annm/1105737695   (156 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   (415 words)

 The Ultimate Nicolas Bourbaki Dog Breeds Information Guide and Reference   (Site not responding. Last check: 2007-10-21) Other notable participants in later days were Laurent Schwartz, Jean-Pierre Serre, Alexander Grothendieck, Samuel Eilenberg, Serge Lang and Roger Godement. The original goal of the group had been to compile an improved mathematical analysis text; it was soon decided that a more comprehensive treatment of all of mathematics was necessary. He pointed to the way axiomatic method can be used as a tool for problem-solving, for example by Alexander Grothendieck. www.dogluvers.com /dog_breeds/Nicolas_Bourbaki   (1745 words)

 Books by P. Cartier, compare prices The Grothendieck Festschrift : A Collection of Articles Written in Honor of the 60th Birthday of Alexander Grothendieck, Vol II Grothendieck Festschrift : Articles in Honor of Alexander Grothendieck on His 60th Birthday The Grothendieck Festschrift : A Collection of Articles Written in Honor of the 60th Birthday of Alexander Grothendieck www.allbookstores.com /author/P_Cartier.html   (181 words)

 References for Grothendieck   (Site not responding. Last check: 2007-10-21) P Cartier, L Illusie, N M Katz, G Laumon, Y Manin and K A Ribet (eds.), The Grothendieck Festschrift (Boston-Basel, 1990). J Dieudonné, A Grothendieck's early work (1950-1960), K-Theory 3 (4) (1989), 299-306. J-P Serre, Rapport au comité Fields sur les travaux de A Grothendieck, K-Theory 3 (3) (1989), 199-204. www-groups.dcs.st-and.ac.uk /history/References/Grothendieck.html   (50 words)

 Recoltes et Semailles   (Site not responding. Last check: 2007-10-21) By December 2002, when I began this translation, 14 years had passed since the distribution, in 1988, of copies of Récoltes et Semailles by Alexander Grothendieck to mathematical colleagues around the world. In my decision to make a rough English translation of the first part of R&S to be placed on the Ferment Magazine website, it is with the hope that this effort will result in other translators coming to the plate and bringing the project to completion. His protestations notwithstanding, it does not have a fraction of the importance of his contribution to mathematics. www.fermentmagazine.org /rands/recoltes1.html   (411 words)

 AoPS Math Forum :: View topic - Crazy Mathematicians As for modern mathematicians, you have to mention Alexander Grothendieck. I would have to strongly disagree with the assertion that Grothendieck is "crazy", absent further evidence. Modern algebraic geometry simply would not be anywhere near where is it today without Grothendieck's ideas. www.artofproblemsolving.com /Forum/viewtopic.php?t=36655   (1369 words)

 The Grothendieck Festschrift: A Collection of Articles Written in Honor of the 60th Birthday of Alexander ... The Grothendieck Festschrift: A Collection of Articles Written in Honor of the 60th Birthday of Alexander Grothendieck:0817634878:Cartier, P.; Illusie, L; Katz, N.M.; Laumon, G.; Manin, Y.; Ribet, K.A.:eCampus.com The Grothendieck Festschrift: A Collection of Articles Written in Honor of the 60th Birthday of Alexander Grothendieck, Vol II Grothendieck Festschrift: Articles in Honor of Alexander Grothendieck on His 60th Birthday www.ecampus.com /bk_detail.asp?isbn=0817634878   (91 words)

 Geometric Galois Actions - Cambridge University Press   (Site not responding. Last check: 2007-10-21) \$55.00 (C) The first of two volumes on anabelian algebraic geometry, this book contains the famous manuscript "Esquisse d'un Programme" (Sketch of a Program) by Alexander Grothendieck. Grothendieck’s ‘Long March through Galois Theory’ L. Schneps; 5. Grothendieck, F. Oort, L. Schneps, F. Pop, T. Oda, B. Teissier, J. Wolfart, V. Adrianov, G. Shabat, P. Lochak, H. Nakamura, D. Harbater, J.-P. Serre www.cup.cam.ac.uk /us/catalogue/print.asp?isbn=0521596424&print=y   (287 words)

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