Alexander Grothendieck (1928 to 2014) pioneered scheme theory, establishing it as the foundation of modern algebraic geometry, and developed the etale and l-adic cohomology theories built on that foundation. He was awarded the Fields Medal in 1966 and is considered by many to be the greatest mathematician of the twentieth century. He was stateless for most of his working life, travelling on a Nansen passport, and was naturalized French only in the early 1980s. In a 1969 paper he showed that a further conjecture Hodge had proposed alongside the Hodge conjecture proper was false for trivial reasons, and supplied a corrected version of it.
Facts
Death PlaceSaint-Lizier, Ariege, France 1 Nationality / CultureStateless for most of his working life, travelling on a Nansen passport; naturalized French in the early 1980s. 1 Defining ContributionScheme theory, established as the foundation of modern algebraic geometry, and the etale and l-adic cohomology theories built on it. 1 Notable WorkRefounded algebraic geometry through scheme theory (EGA, SGA) and topos theory; unified algebraic geometry with number theory and topology; foundational contributions to commutative algebra, homological algebra, sheaf theory and category theory 1 Connections
Associated With
Grothendieck showed that a further conjecture Hodge proposed alongside the Hodge conjecture proper was false for trivial reasons, and gave a corrected version of it.
Source Clay Mathematics Institute
Attributed Works
Source Picard Group (Wikipedia)
Source Scheme (mathematics) (Wikipedia)
Conjectures Posed
In Branch
Source Alexander Grothendieck (Wikipedia)
Source Alexander Grothendieck (Wikipedia)
Mentored
Source Max Karoubi (Wikipedia)
Source Pierre Deligne (Wikipedia)
Principal Result
Source Ax-Grothendieck Theorem (Wikipedia)
Proofs Credited
In the Other Atlases
Nationality
Also in Geography Atlas: the nationality of this subject.
Source Alexander Grothendieck (Wikipedia)tier 2
Also in Geography Atlas: the nationality of this subject.
Source Alexander Grothendieck (Wikipedia)tier 2
Sources
1. Alexander Grothendieck (Wikipedia)
WikipediaInfobox: birth_place
Berlin, Prussia, Germany
Citizenship
Thus, he became a stateless person for at least the majority of his working life and he traveled on a Nansen passport.
Lead section
His research extended the scope of the field and added elements of commutative algebra, homological algebra, sheaf theory, and category theory to its foundations, while his so-called "relative" perspective led to revolutionary advances in many areas of pure mathematics.
Lead section, gender reference
His research extended the scope of the field and added elements of commutative algebra, homological algebra, sheaf theory, and category theory to its foundations, while his so-called "relative" perspective led to revolutionary advances in many areas of pure mathematics.
View the Source 2. International Mathematical Union: Fields Medal
International Mathematical UnionThe Fields Medalists, chronologically listedQuote, The Fields Medalists, chronologically listed
Alexander Grothendieck
Clay Mathematics Institute
Clay Mathematics InstituteAssociated With: Hodge Conjecture, Section 2, Remark (vi), p. 2Quote, Associated With: Hodge Conjecture, Section 2, Remark (vi), p. 2
Grothendieck observed that this further conjecture is trivially false, and gave a corrected version of it in [5].
Ax-Grothendieck Theorem (Wikipedia)
Principal Result: Ax-Grothendieck Theorem, Lead sentence of the article on the resultQuote, Principal Result: Ax-Grothendieck Theorem, Lead sentence of the article on the result
In mathematics, the Ax-Grothendieck theorem is a result about injectivity and surjectivity of polynomials that was proved independently by James Ax and Alexander Grothendieck.
Pierre Deligne (Wikipedia)
Mentored: Pierre Deligne, Early life and educationQuote, Mentored: Pierre Deligne, Early life and education
under the supervision of Alexander Grothendieck
Max Karoubi (Wikipedia)
Mentored: Max Karoubi, Lead, second supervisorQuote, Mentored: Max Karoubi, Lead, second supervisor
In 1967, he received his Ph.D. in mathematics (Doctorat d'État) from the University of Paris, under the supervision of Henri Cartan and Alexander Grothendieck.
Scheme (mathematics) (Wikipedia)
Wikimedia FoundationAttributed Works: Scheme (Mathematics), LeadQuote, Attributed Works: Scheme (Mathematics), Lead
Scheme theory was introduced by Alexander Grothendieck in 1960 in his treatise Éléments de géométrie algébrique (EGA); one of its aims was developing the formalism needed to solve deep problems of algebraic geometry, such as the Weil conjectures (the last of which was proved by Pierre Deligne).
Picard Group (Wikipedia)
Attributed Works: Picard Group, Lead sectionQuote, Attributed Works: Picard Group, Lead section
in particular in the duality theory of abelian varieties. It was constructed by Grothendieck (1962), and also described by Mumford (1966) and Kleiman
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