Prescribed subintegral extensions of local Noetherian domains

Flat local morphisms of rings with prescribed depth and dimension

For pairs of integers (n,m) and (d,e) satisfying some nedesary conditions, we construct a local flat ring morphism of noetherian local rings u:A -->B such that dim(A)=n, depth(A)=d, dim(B)=m, depth(B)=e.

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 t…

How to construct a closed subscheme, or a coherent subsheaf, with prescribed germs

We show that a closed subscheme of a given locally noetherian scheme can be constructed by prescribing it germs at all points of the ambient scheme in a manner consistent with specialization of points, provided the resulting set of all associated points of all the germs is locally finite. More generally, we prove a similar result for constructing a coherent subsheaf of a coherent sheaf by prescribing its stalks at all points in a manner consistent with specializations of points, again provided the set of all associated points of all the corresponding local quotients is locally finite. On any l…

有限射影维数与Jorgensen的问题

Finite projective dimension and a question of Jorgensen

本文通过广义局部上同调相关的谱序列方法研究有限生成模的有限射影维数，解决Jorgensen十五年前关于完全交局部环上射影维数上界的问题，并探讨其他同调维数的相关结果。