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Title:The Grade Conjecture and asymptotic intersection multiplicity
Author(s):Beder, Jesse
Director of Research:Dutta, Sankar P.
Doctoral Committee Chair(s):Griffith, Phillip A.
Doctoral Committee Member(s):Dutta, Sankar P.; Schenck, Henry K.; Haboush, William J.
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):commutative algebra
grade conjecture
characteristic p
frobenius
intersection multiplicity
Abstract: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 $x_1, \ldots, x_r$ 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.
Issue Date:2013-02-03
URI:http://hdl.handle.net/2142/42274
Rights Information:Copyright 2012 Jesse Beder
Date Available in IDEALS:2013-02-03
Date Deposited:2012-12


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