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Title The Grade Conjecture and asymptotic intersection multiplicity
Publication Date
Date Accessioned
Degree PhD
Discipline/Department 0439
Degree Level doctoral
University/Publisher University of Illinois – Urbana-Champaign
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.
Subjects/Keywords commutative algebra; grade conjecture; characteristic p; frobenius; intersection multiplicity
Contributors Dutta, Sankar P. (advisor); Griffith, Phillip A. (Committee Chair); Dutta, Sankar P. (committee member); Schenck, Henry K. (committee member); Haboush, William J. (committee member)
Language en
Rights Copyright 2012 Jesse Beder
Country of Publication us
Record ID handle:2142/42274
Repository uiuc
Date Indexed 2020-03-09
Grantor University of Illinois at Urbana-Champaign
Issued Date 2013-02-03 19:29:58

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