We prove that, modulo any power of a prime $ p $, the absolute integral closure of an
excellent noetherian domain is Cohen-Macaulay. A graded analog is also established …

The Grothendieck–Serre conjecture predicts that every generically trivial torsor under a
reductive group scheme G over a regular local ring R is trivial. We settle it in the case when …

We show that the v-sheaf local models of Scholze and Weinstein are unibranch. In
particular, this proves that the scheme-theoretic local models defined in Anschütz, Gleason …

We prove the relative Grauert-Riemenschneider vanishing, Kawamata-Viehweg vanishing,
and Koll\'ar injectivity theorems for proper morphisms of schemes of equal characteristic …

In this paper, we prove Faltings' annihilator theorem for complexes over a CM-excellent ring.
As an application, we give a complete classification of the t-structures of the bounded …

La conjecture du facteur direct (théorème 1.1 ci-dessous) est un énoncé d'algèbre
commutative presque aussi élémentaire que le Théorème de Fermat et qui est resté ouvert …

We show that for each algebraic space that is separated and of finite type over a field, and
whose affinization is connected and reduced, there is a universal morphism to a para …

Let (R, m) be a Noetherian local ring and M be a finitely generated R-module. In this paper,
we construct almost p-standard systems of parameters (a strict subclass of d-sequences) of …

Let $ R $ be a commutative noetherian ring. Denote by $\operatorname {mod} R $ the
category of finitely generated $ R $-modules, by $\operatorname {D^ b}(R) $ the bounded …

Let R be a commutative Noetherian ring, I an ideal of R, and M a finitely generated R-
module. The asymptotic behavior of the quotient modules M/InM of M is an actively studied …