The Grade Conjecture and asymptotic intersection multiplicity

In this thesis, we study Peskine and Szpiro's Grade Conjecture and its connection with asymptotic intersection multiplicity \chi_\infty. Given an $A$-module $M$ of finite projective dimension and a system of parameters x₁, \ldots, x_r for $M$, we show, under certain assumptions on $M$, that \chi_\infty(M, A/\underline{x}) > 0. We also give a necessary and sufficient condition on $M$ for the existence of a system of parameters $\underline{x}$ with \chi_\infty(M, A/\underline{x}) > 0. We then prove that if the Grade Conjecture holds for a given module $M$, then there is a system of parameters $\underline{x}$ such that \chi_\infty(M, A/\underline{x}) > 0. We also prove the Grade Conjecture for complete equidimensional local rings in any characteristic.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2013

Author dc:creator

• Beder, Jesse

Contributors dc:contributor

• Dutta, Sankar P.
• Griffith, Phillip A.
• Schenck, Henry K.
• Haboush, William J.

• commutative algebra
• grade conjecture
• characteristic p
• frobenius
• intersection multiplicity

Statement dc:rights

• Copyright 2012 Jesse Beder

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/42274

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/42274