In mathematics, the Grothendieck existence theorem, introduced by Grothendieck (1961, section 5), gives conditions that enable one to lift infinitesimal...

connection Grothendieck construction Grothendieck duality Grothendieck existence theorem Grothendieck fibration Grothendieck's Galois theory Grothendieck group...

Alexander Grothendieck, later Alexandre Grothendieck in French (/ˈɡroʊtəndiːk/; German: [ˌalɛˈksandɐ ˈɡʁoːtn̩ˌdiːk] ; French: [ɡʁɔtɛndik]; 28 March 1928 –...

ample line bundle L {\displaystyle {\mathcal {L}}} . It is a theorem of Grothendieck's that the functors Q u o t E / X / S Φ , L {\displaystyle {\mathcal...

to proving the Grothendieck duality theorem in algebraic geometry. Jacob Lurie has proved a version of the Brown representability theorem for the homotopy...

thesis that the hard part of the proof can be presented as the Model Existence Theorem (published in 1949). Henkin's proof was simplified by Gisbert Hasenjaeger...

{\displaystyle p.} One consequence is the following special case of the Ax–Grothendieck theorem: all injective complex polynomials C n → C n {\displaystyle \mathbb...

Hartshorne 1970. Serre 1956. Grothendieck & Raynaud 2002, EXPOSE XII.. Neeman 2007. Grothendieck & Raynaud 2002, EXPOSE XII, 4. Théorèmes de comparaison cohomologique...

McLarty, Colin (2010). "What does it take to prove Fermat's last theorem? Grothendieck and the logic of number theory". The Review of Symbolic Logic. 13...

connected for all s ∈ S {\displaystyle s\in S} . The theorem also leads to the Grothendieck existence theorem, which gives an equivalence between the category...