2026-09-19T23:19:17Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/42274 2023-07-11 col_2142_5131 col_2142_16340 com_2142_5130 com_2142_16339 com_2142_8903

Dutta, Sankar P. Griffith, Phillip A. Dutta, Sankar P. Schenck, Henry K. Haboush, William J. Beder, Jesse 2013-02-03T19:29:58Z 2013-02-03T19:29:58Z 2012-12 2013-02-03T19:29:58Z 2012-12 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. Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2012-07-18T12:47:30Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 7 uiucthesis.cls: 17745 bytes, checksum: 2d97b89eb400b38a73a704ef757b5460 (MD5) 4-main.tex: 13848 bytes, checksum: fe7bd516281d0223ea8dbba70594ee4a (MD5) 3-grade-conjecture.tex: 42579 bytes, checksum: 78fc7491eedac22dd5c29aa607e86f24 (MD5) 2-background.tex: 28120 bytes, checksum: 0f5e758e7192bb82a169f4a12dfad857 (MD5) 1-introduction.tex: 7401 bytes, checksum: 2843074c02d5facfcd9ec77f66b995ef (MD5) thesis.tex: 5772 bytes, checksum: 2d8e71e41a98a106ae13e84347eb3c0a (MD5) Beder_Jesse.pdf: 390679 bytes, checksum: b9c2a0000d711c1da1c5e19e390fe989 (MD5) Made available in DSpace on 2013-02-03T19:29:58Z (GMT). No. of bitstreams: 8 Jesse_Beder.pdf: 391710 bytes, checksum: d4869d30a03e1b5d0a0c6ad5588aafb8 (MD5) license.txt: 4058 bytes, checksum: 684c420eec1bd160f21b9ab5d0518bb0 (MD5) thesis.tex: 5746 bytes, checksum: ac9ae6b72a392c17ca3a7472fc4811d5 (MD5) 1-introduction.tex: 7401 bytes, checksum: 2843074c02d5facfcd9ec77f66b995ef (MD5) 2-background.tex: 28120 bytes, checksum: 0f5e758e7192bb82a169f4a12dfad857 (MD5) 3-grade-conjecture.tex: 42579 bytes, checksum: 78fc7491eedac22dd5c29aa607e86f24 (MD5) 4-main.tex: 13848 bytes, checksum: fe7bd516281d0223ea8dbba70594ee4a (MD5) uiucthesis.cls: 17745 bytes, checksum: 2d97b89eb400b38a73a704ef757b5460 (MD5) http://hdl.handle.net/2142/42274 en Copyright 2012 Jesse Beder commutative algebra grade conjecture characteristic p frobenius intersection multiplicity The Grade Conjecture and asymptotic intersection multiplicity text Mathematics 1257 Mathematics 0439 University of Illinois at Urbana-Champaign Dissertation Ph.D. PHD:Mathematics -UIUC 10KS0439PHD