" Ha habido muy pocas exposiciones sistemáticas de la teoría de las categorías derivadas
desde su inicio en el trabajo de Grothendieck y Verdier en la década de 1960. Este libro es …

A notion of rigidity with respect to an arbitrary semidualizing complex C over a commutative
noetherian ring R is introduced and studied. One of the main results characterizes C-rigid …

We consider commutative DG rings (better known as nonpositive strongly commutative
associative unital DG algebras). For such a DG ring $ A $ we define the notions of perfect …

Semi-Infinite Geometry is a theory of" doubly infinite-dimensional" geometric or topological
objects. In this book the author explains what should be meant by an algebraic variety of …

Kuznetsov has conjectured that Pfaffian varieties should admit noncommutative crepant
resolutions which satisfy his Homological Projective Duality. We prove half the cases of this …

A quasi-coherent ringed scheme is a pair (X, A), where X is a scheme, and A is a
noncomutative quasi-coherent O _X-ring. We introduce dualizing complexes over quasi …

Abstract Let A→ B be a homomorphism of commutative rings. The squaring operation is a
functor Sq B/A from the derived category D (B) of complexes of B-modules into itself. This …

We show that any separated essentially finite-type map f of noetherian schemes globally
factors as f= hi where i is an injective localization map and ha separated finite-type map. In …

Let $ A $ be a commutative ring, $ B $ a commutative $ A $-algebra and $ M $ a complex of
$ B $-modules. We begin by constructing the square $\operatorname {Sq} _ {B/A} M $, which …

We prove basic facts about reflexivity in derived categories over noetherian schemes, and
about related notions such as semidualizing complexes, invertible complexes, and …