Grothendieck in a sentence

Grothendieck also saw how to phrase the definition of covering abstractly; this is where the definition of a Grothendieck topology comes from.

Alexander Grothendieck teaching at the elite Institut des Hautes Études Scientifiques in the 1960s.

Alexander was permitted to live, separated from his mother, Luca Barbieri Viale, 'Alexander Grothendieck:entusiasmo e creatività,' in C. Bartocci, R. Betti, A. Guerraggio, R. Lucchetti (eds.

As Cartier puts it, Grothendieck came to find Bures-sur-Yvette "une cage dorée" ("a golden cage").

Biology interested Grothendieck much more than physics, and he organized some seminars on biological topics.

Conversely, there are Grothendieck topologies which do not come from topological spaces.

Grothendieck also gave axioms AB6) and AB6*).

Grothendieck conjectured that and must be different whenever X and Y are infinite-dimensional Banach spaces.

Grothendieck himself practically ceased publication of papers through the conventional, learned journal route.

Grothendieck laid a new foundation for algebraic geometry by making intrinsic spaces ("spectra") and associated rings the primary objects of study.

Grothendieck pretopologies In fact, it is possible to put these axioms in another form where their geometric character is more apparent, assuming that the underlying category C contains certain fibered products.

Grothendieck took them to a higher level of abstraction and turned them into a key organising principle of his theory.

However, if an inaccessible cardinal κ is assumed, then the sets of smaller rank form a model of ZF (a Grothendieck universe ), and its subsets can be thought of as "classes".

However, if the original monoid has an absorbing element then its Grothendieck group is the trivial group.

However, most modern algebraic geometry texts starting with Alexander Grothendieck's foundational EGA use the convention in this article.

However simple examples such as the indiscrete topological space show that not all topological spaces can be expressed using Grothendieck topologies.

If the collection of all covering families satisfies certain axioms, then we say that they form a Grothendieck pretopology.

In an obituary David Mumford and John Tate wrote: Although mathematics became more and more abstract and general throughout the 20th century, it was Alexander Grothendieck who was the greatest master of this trend.

In Chambon, Grothendieck attended the Collège Cévenol (now known as the Le Collège-Lycée Cévenol International ), a unique secondary school founded in 1938 by local Protestant pacifists and anti-war activists.

In it, Cartier notes that as the son of an antimilitary anarchist and one who grew up among the disenfranchised, Grothendieck always had a deep compassion for the poor and the downtrodden.