Back to Commutative Algebra Seminar: Spring 2017
Commutative Algebra Seminar
Date: Wednesday, Mar 8, 2017
Time: 3:10PM - 4:00PM
Location: LCB 215
Tsutomu Nakamura
Okayama University, Japan
Title |
Local homology functors with cosupports in general subsets of Spec R |
Abstract |
Let R be a commutative Noetherian ring. In this talk, we introduce the local homology functor lambda^W with cosupport in a subset W of Spec R. If W is equal to a closed subset V(I) for an ideal I of R, then lambda^W coincides with an ordinary local homology functor, which is isomorphic to the left derived functor of I-adic completion functor. We show several results about lambda^W, where W is not necessarily closed or specialization-closed. As an application, we can give a simple proof of a classical theorem by Raynaud and Gruson, which states that the projective dimension of a flat R-module is less than or equal to the Krull dimension of R. This talk is based on a joint work with Yuji Yoshino. |
Commutative Algebra