17 citations · 30 across the 5 of their papers we have counts for
9 papers
Perfectoid spaces and the homological conjectures
Yves Andre
This is a survey of recent advances in commutative algebra, especially in mixed characteristic, obtained by using the theory of perfectoid spaces. An explanation of these technique…
Weak functoriality of Cohen-Macaulay algebras
Yves Andre
We prove the weak functoriality of (big) Cohen-Macaulay algebras, which controls the whole skein of "homological conjectures" in commutative algebra [H1][HH2]. Namely, for any loca…
La conjecture du facteur direct
Yves Andre
Building on his reduction to the case of an unramified complete regular local ring R of mixed characteristic, we propose a proof in the framework of P. Scholze's perfectoid theory.…
Solution algebras of differential equations and quasi-homogeneous varieties: a new differential Galois correspondence
Yves Andre
We develop a new connection between Differential Algebra and Geometric Invariant Theory, based on an anti-equivalence of categories between solution algebras associated to a linear…
Galois theory, motives and transcendental numbers
Yves Andre
From its early beginnings up to nowadays, algebraic number theory has evolved in symbiosis with Galois theory: indeed, one could hold that it consists in the very study of the abso…
Ambiguity theory, old and new
Yves Andre
This is a introductory survey of some recent developments of "Galois ideas" in Arithmetic, Complex Analysis, Transcendental Number Theory and Quantum Field Theory, and of some of t…