Growth of Betti numbers and cohomology operators defined by a deformation

Li-Chuan Sun, Purdue University

Abstract

In chapter 1, we prove for modules over local rings of small embedding codimension or small linkage number that radius of convergence of the Poincare series is less than one, then the Betti sequence is eventually nondecreasing and has strong exponential growth. In chapter 2, we construct cohomology operators $\chi\sb{j}$: Ext$\sbsp{R}{i}(M,N)\to {\rm Ext}\sbsp{R}{i+2}(M,N)$ and $\chi\sb{j}$: To$\sbsp{i}{R}(M,N)\to {\rm Tor}\sbsp{i-2}{R}(M,N)$ over commutative rings of the form $R = Q/(x\sb1,\cdots,x\sb{n})$ for some Koszul regular set $(x\sb1,\cdots,x\sb{n})\subset Q$. Various properties of these operators are discussed. They are compared to those introduced earlier by Gulliksen, Eisenbud, Mehta, and Avramov.

Degree

Ph.D.

Advisors

Avramov, Purdue University.

Subject Area

Mathematics

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