Back to Algebraic Geometry Seminar: Fall 2015
Algebraic Geometry Seminar
Date: Tuesday, Nov 17, 2015
Time: 3:30PM - 4:30PM
Location: JFB 102
Linquan Ma
University of Utah
Title |
Lim Cohen-Macaulay sequence |
Abstract |
We introduce the notion of a lim Cohen-Macaulay sequence of nonzero Noetherian modules {M_n}_n over a local ring R. The definition is phrased in terms of asymptotic length of higher Kozul homology of M_n with respect to one (equivalently, every) system of parameters. We prove that if lim Cohen-Macaulay sequences exist for the quotients of a regular local ring R by its prime ideals, then Serre’s conjecture on positivity of intersection multiplicities holds for R. We also show that if R has such a sequence, one can use it to define a closure operation on ideals and submodules of finitely generated modules over R. In positive characteristic, lim Cohen-Macaulay sequences exist, and tight closure is a closure of operation that arises in this way. Quite generally, these closure operations enable one to construct big Cohen-Macaulay modules. Joint work with Bhargav Bhatt and Mel Hochster. |
Algebraic Geometry