645 research outputs found
Cohomology over complete intersections via exterior algebras
A general method for establishing results over a commutative complete
intersection local ring by passing to differential graded modules over a graded
exterior algebra is described. It is used to deduce, in a uniform way, results
on the growth of resolutions of complexes over such local rings.Comment: 18 pages; to appear in "Triangulated categories (Leeds, 2006)", LMS
lecture notes series
Constructing modules with prescribed cohomological support
A cohomological support, Supp_A(M), is defined for finitely generated modules
M over an left noetherian ring R, with respect to a ring A of central
cohomology operations on the derived category of R-modules. It is proved that
if the A-module Ext^R(M,M) is noetherian and Ext_i^R(M,R)=0 for i>>0, then
every closed subset of Supp_A(M) is the support of some finitely generated
R-module. This theorem specializes to known realizability results for varieties
of modules over group algebras, over local complete intersections, and over
finite dimensional algebras over a field. The theorem is also used to produce
large families of finitely generated modules of finite projective dimension
over commutative local noetherian rings.Comment: To appear in the Illinois Journal of Mathematics, the issue honoring
Phillip Griffith. Revised version has 18 pages. A word (the first one) has
been added to the title and the material has been reorganized into seven
sections, in place of the original six. There are, however, no changes of any
substanc
Reflexivity and rigidity for complexes, II: Schemes
We prove basic facts about reflexivity in derived categories over noetherian
schemes; and about related notions such as semidualizing complexes, invertible
complexes, and Gorenstein-perfect maps. Also, we study a notion of rigidity
with respect to semidualizing complexes, in particular, relative dualizing
complexes for Gorenstein-perfect maps. Our results include theorems of
Yekutieli and Zhang concerning rigid dualizing complexes on schemes. This work
is a continuation of part I, which dealt with commutative rings.Comment: 40 page
Subadditivity of syzygies of Koszul algebras
Estimates are obtained for the degrees of minimal syzygies of quotient
algebras of polynomial rings. For a class that includes Koszul algebra in
almost all characteristics, these degrees are shown to increase by at most 2
from one syzygy module to the next one. Even slower growth is proved if, in
addition, the algebra satisfies Green and Lazarsfeld's condition N_q with q >
1.Comment: 19 page
Quasi-complete intersection homomorphisms
Extending a notion defined for surjective maps by Blanco, Majadas, and
Rodicio, we introduce and study a class of homomorphisms of commutative
noetherian rings, which strictly contains the class of locally complete
intersection homomorphisms, while sharing many of its remarkable properties.Comment: Final version, to appear in the special issue of Pure and Applied
Mathematics Quarterly dedicated to Andrey Todorov. The material in the first
four sections has been reorganized and slightly expande
- …