Constructing modules with prescribed cohomological support
By L. Avramov, S. Iyengar. 2007
55 citations recorded by the source corpus.
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.
Subfields: Algebra and Number Theory, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/180cbbf652535dee0ea99aa0fab97a2cb5220c7e
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In Algebra and Number Theory
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Citations in the corpus
- Classification of resolving subcategories and grade consistent functions (2012, methodology): “imple example, let Rbe a local complete intersection and M,Nbe modules of finite length. Then Ncan be built from Musing syzygies, extensions and direct summands if and only if the support variety (see [6]) of Nis contained in that of M. Support varieties can be computed using a computer program like ”