This book is a comprehensive treatment of the representation theory of maximal Cohen-
Macaulay (MCM) modules over local rings. This topic is at the intersection of commutative …

We define a notion of total acyclicity for complexes of flat quasi-coherent sheaves on a semi-
separated noetherian scheme, and study these complexes using the pure derived category …

Let $ G $ be a semisimple algebraic group over the complex numbers and $ K $ be a
connected reductive group mapping to $ G $ so that the Lie algebra of $ K $ gets identified …

We show that the derived category of coherent sheaves on the quotient stack of the affine
plane by a finite small subgroup of the general linear group is obtained from the derived …

The punctual Hilbert scheme has been known since the early days of algebraic geometry in
EGA style. Indeed it is a very particular case of the Grothendieck's Hilbert scheme which …

arXiv:0911.4541v1 [math.AC] 24 Nov 2009 Page 1 arXiv:0911.4541v1 [math.AC] 24 Nov 2009
REMARKS ON NON-COMMUTATIVE CREPANT RESOLUTIONS OF COMPLETE …

Proceedings of the International Congress of Mathematicians (ICM 2018) : TILTING COHEN–MACAULAY
REPRESENTATIONS Page 1 P . I . C . M . – 2018 Rio de Janeiro, Vol. 2 (125–162) TILTING …

This paper is devoted to algebro-geometric study of infinite dimensional Lie bialgebras,
which arise from solutions of the classical Yang–Baxter equation. We regard trigonometric …

Let $ R $ be a Cohen-Macaulay ring and $ M $ a maximal Cohen-Macaulay $ R $-module.
Inspired by recent striking work by Iyama, Burban-Iyama-Keller-Reiten and van den Bergh …

Let R be a complete local hypersurface over an algebraically closed field of characteristic
different from two, and suppose that R has countable Cohen–Macaulay (CM) representation …