Familie en kindertijd[ bewerken brontekst bewerken ] Hanka Grothendieck, zijn moeder Alexander Grothendieck werd in in Berlijn in een anarchistisch milieu geboren. Zijn Duitse moeder, de schrijfster en journaliste Johanna Hanka Grothendieck, stamde uit een uit een voorname Hamburgse , protestantse familie. Hij had Chassidische wortels en had in Rusland gevangengezeten voordat hij in naar Duitsland kwam. In Berlijn kwam hij onder de schuilnaam Alexander Tanarow als fotograaf aan de kost.
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Life[ edit ] Family and childhood[ edit ] Grothendieck was born in Berlin to anarchist parents. His father, Alexander "Sascha" Schapiro also known as Alexander Tanaroff , had Hasidic Jewish roots and had been imprisoned in Russia before moving to Germany in , while his mother, Johanna "Hanka" Grothendieck, came from a Protestant family in Hamburg and worked as a journalist. Both had broken away from their early backgrounds in their teens.
They left Grothendieck in the care of Wilhelm Heydorn, a Lutheran pastor and teacher   in Hamburg. Shortly afterwards his father was interned in Le Vernet. Once Alexander managed to escape from the camp, intending to assassinate Hitler. After three years of increasingly independent studies there, he went to continue his studies in Paris in By , he set this subject aside in order to work in algebraic geometry and homological algebra.
The prospect did not worry him, as long as he could have access to books. He was, however, able to play a dominant role in mathematics for around a decade, gathering a strong school. Closely linked to these cohomology theories, he originated topos theory as a generalisation of topology relevant also in categorical logic. He also provided an algebraic definition of fundamental groups of schemes and more generally the main structures of a categorical Galois theory. As a framework for his coherent duality theory he also introduced derived categories , which were further developed by Verdier.
He gave lectures on category theory in the forests surrounding Hanoi while the city was being bombed, to protest against the Vietnam War. The Grothendieck Festschrift, published in , was a three-volume collection of research papers to mark his sixtieth birthday in By the late s, he had started to become interested in scientific areas outside mathematics. The group published a bulletin and was dedicated to antimilitary and ecological issues, and also developed strong criticism of the indiscriminate use of science and technology.
He formally retired in , a few years after having accepted a research position at the CNRS. In , stimulated by correspondence with Ronald Brown and Tim Porter at Bangor University , Grothendieck wrote a page manuscript titled Pursuing Stacks , starting with a letter addressed to Daniel Quillen. This letter and successive parts were distributed from Bangor see External links below.
Within these, in an informal, diary-like manner, Grothendieck explained and developed his ideas on the relationship between algebraic homotopy theory and algebraic geometry and prospects for a noncommutative theory of stacks. The manuscript, which is being edited for publication by G. Written in , this latter opus of about pages further developed the homotopical ideas begun in Pursuing Stacks.
It describes new ideas for studying the moduli space of complex curves. He complains about what he saw as the "burial" of his work and betrayal by his former students and colleagues after he had left the community.
He wrote that established mathematicians like himself had no need for additional financial support and criticized what he saw as the declining ethics of the scientific community, characterized by outright scientific theft that, according to him, had become commonplace and tolerated.
The letter also expressed his belief that totally unforeseen events before the end of the century would lead to an unprecedented collapse of civilization. In it, he described his encounters with a deity and announced that a "New Age" would commence on 14 October Local villagers helped sustain him with a more varied diet after he tried to live on a staple of dandelion soup.
Thus they became among "the last members of the mathematical establishment to come into contact with him". He asks that none of his work be reproduced in whole or in part and that copies of this work be removed from libraries. In , aged ten, he moved to France as a refugee. Records of his nationality were destroyed in the fall of Germany in and he did not apply for French citizenship after the war. He thus became a stateless person for at least the majority of his working life, traveling on a Nansen passport.
She died in from the tuberculosis that she contracted in camps for displaced persons. His key contributions include topological tensor products of topological vector spaces , the theory of nuclear spaces as foundational for Schwartz distributions , and the application of Lp spaces in studying linear maps between topological vector spaces.
Grothendieck took them to a higher level of abstraction and turned them into a key organising principle of his theory. He shifted attention from the study of individual varieties to the relative point of view pairs of varieties related by a morphism , allowing a broad generalization of many classical theorems.
In , he applied the same thinking to the Riemann—Roch theorem , which had already recently been generalized to any dimension by Hirzebruch. This result was his first work in algebraic geometry. His foundational work on algebraic geometry is at a higher level of abstraction than all prior versions. He adapted the use of non-closed generic points , which led to the theory of schemes.
He also pioneered the systematic use of nilpotents. His theory of schemes has become established as the best universal foundation for this field, because of its expressiveness as well as technical depth. In that setting one can use birational geometry , techniques from number theory , Galois theory and commutative algebra , and close analogues of the methods of algebraic topology , all in an integrated way.
His influence spilled over into many other branches of mathematics, for example the contemporary theory of D-modules. It also provoked adverse reactions, with many mathematicians seeking out more concrete areas and problems. Weil realized that to prove such a connection one needed a new cohomology theory, but neither he nor any other expert saw how to do this until such a theory was found by Grothendieck.
The Grothendieck Festschrift
The Grothendieck Festschrift, Volume II