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Bernstein-Sato Theory in Positive Characteristic.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Bernstein-Sato Theory in Positive Characteristic./
作者:	Quinlan, Eamon M.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2021,
面頁冊數:	92 p.
附註:	Source: Dissertations Abstracts International, Volume: 83-05, Section: B.
Contained By:	Dissertations Abstracts International83-05B.
標題:	Mathematics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28846645
ISBN:	9798471105973

Bernstein-Sato Theory in Positive Characteristic.
Quinlan, Eamon M.

Bernstein-Sato Theory in Positive Characteristic. - Ann Arbor : ProQuest Dissertations & Theses, 2021 - 92 p.

Source: Dissertations Abstracts International, Volume: 83-05, Section: B.

Thesis (Ph.D.)--University of Michigan, 2021.

This item must not be sold to any third party vendors.

Given a holomorphic function f, its Bernstein-Sato polynomial is a classical invariant that detects the singularities of the zero locus of f in very subtle ways; for example, its roots recover the log-canonical threshold of f and the eigenvalues of the monodromy action on the cohomology of the Milnor fibre. In this thesis we continue the work of Bitoun and Mustata to develop an analogue of this invariant in positive characteristic. More concretely, we develop a notion of Bernstein-Sato polynomial for arbitrary ideals (which, over the complex numbers, was done by Budur, Mustata and Saito), we show that its roots are always rational and negative and that they encode some information about the F-jumping numbers. We also prove that for monomial ideals we can recover the roots of the classical Bernstein-Sato polynomial from this characteristic-p version.

ISBN: 9798471105973Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Bernstein-Sato polynomial

Bernstein-Sato Theory in Positive Characteristic.
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245 1 0 $a Bernstein-Sato Theory in Positive Characteristic.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2021
300 $a 92 p.
500 $a Source: Dissertations Abstracts International, Volume: 83-05, Section: B.
500 $a Advisor: Smith, Karen.
502 $a Thesis (Ph.D.)--University of Michigan, 2021.
506 $a This item must not be sold to any third party vendors.
506 $a This item must not be added to any third party search indexes.
520 $a Given a holomorphic function f, its Bernstein-Sato polynomial is a classical invariant that detects the singularities of the zero locus of f in very subtle ways; for example, its roots recover the log-canonical threshold of f and the eigenvalues of the monodromy action on the cohomology of the Milnor fibre. In this thesis we continue the work of Bitoun and Mustata to develop an analogue of this invariant in positive characteristic. More concretely, we develop a notion of Bernstein-Sato polynomial for arbitrary ideals (which, over the complex numbers, was done by Budur, Mustata and Saito), we show that its roots are always rational and negative and that they encode some information about the F-jumping numbers. We also prove that for monomial ideals we can recover the roots of the classical Bernstein-Sato polynomial from this characteristic-p version.
590 $a School code: 0127.
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical mathematics. $3 3173530
653 $a Bernstein-Sato polynomial
653 $a b-function
653 $a Positive characteristic
690 $a 0405
690 $a 0642
710 2 $a University of Michigan. $b Mathematics. $3 3185260
773 0 $t Dissertations Abstracts International $g 83-05B.
790 $a 0127
791 $a Ph.D.
792 $a 2021
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28846645