Test ideals via algebras of p−e-linear maps

Publikationstyp:
Zeitschriftenaufsatz
Metadaten:
Autoren
  • Manuel Blickle
Sammlungen
  • metadata
ISSN
1056-3911
Ausgabe der Veröffentlichung
1
Zeitschrift
Journal of algebraic geometry
Schlüsselwörter
  • 510 Mathematik
  • 510 Mathematics
Sprache
eng
Paginierung
Seiten: 49 - 83
Datum der Veröffentlichung
2013
Herausgeber
Univ. Pr.
Herausgeber URL
http://dx.doi.org/10.1090/S1056-3911-2012-00576-1
Datum der Datenerfassung
2020
Datum, an dem der Datensatz öffentlich gemacht wurde
2020
Zugang
Public
Titel
Test ideals via algebras of p−e-linear maps
Ausgabe der Zeitschrift
22

Datenquelle: METADATA.UB

Andere Metadatenquellen:
Autoren
  • Manuel Blickle
Autoren-URL
https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=fis-test-1&SrcAuth=WosAPI&KeyUT=WOS:000344048600004&DestLinkType=FullRecord&DestApp=WOS_CPL
eISSN
1534-7486
Externe Identifier
  • Clarivate Analytics Document Solution ID: AS1NX
ISSN
1056-3911
Ausgabe der Veröffentlichung
1
Zeitschrift
JOURNAL OF ALGEBRAIC GEOMETRY
Paginierung
49 - 83
Datum der Veröffentlichung
2013
Status
Published
Titel
TEST IDEALS VIA ALGEBRAS OF <i>p</i><SUP>-e</SUP>-LINEAR MAPS
Sub types
  • Article
Ausgabe der Zeitschrift
22

Datenquelle: Web of Science (Lite)

Abstract
<p>Building on previous work of Schwede, Böckle, and the author, we study test ideals by viewing them as minimal objects in a certain class of modules, called <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper F"> <mml:semantics> <mml:mi>F</mml:mi> <mml:annotation encoding="application/x-tex">F</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-pure modules, over algebras of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="p Superscript negative e"> <mml:semantics> <mml:msup> <mml:mi>p</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>−<!-- − --></mml:mo> <mml:mi>e</mml:mi> </mml:mrow> </mml:msup> <mml:annotation encoding="application/x-tex">p^{-e}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-linear operators. We develop the basics of a theory of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper F"> <mml:semantics> <mml:mi>F</mml:mi> <mml:annotation encoding="application/x-tex">F</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-pure modules and show an important structural result, namely that <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper F"> <mml:semantics> <mml:mi>F</mml:mi> <mml:annotation encoding="application/x-tex">F</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-pure modules have finite length. This result is then linked to the existence of test ideals and leads to a simplified and generalized treatment, also allowing us to define test ideals in non-reduced settings.</p> <p>Combining our approach with an observation of Anderson on the contracting property of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="p Superscript negative e"> <mml:semantics> <mml:msup> <mml:mi>p</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>−<!-- − --></mml:mo> <mml:mi>e</mml:mi> </mml:mrow> </mml:msup> <mml:annotation encoding="application/x-tex">p^{-e}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-linear operators yields an elementary approach to test ideals in the case of affine <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="k"> <mml:semantics> <mml:mi>k</mml:mi> <mml:annotation encoding="application/x-tex">k</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-algebras, where <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="k"> <mml:semantics> <mml:mi>k</mml:mi> <mml:annotation encoding="application/x-tex">k</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is an <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper F"> <mml:semantics> <mml:mi>F</mml:mi> <mml:annotation encoding="application/x-tex">F</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-finite field. As a byproduct, one obtains a short and completely elementary proof of the discreteness of the jumping numbers of test ideals in a generality that extends most cases known so far; in particular, one obtains results beyond the <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="double-struck upper Q"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="double-struck">Q</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">\mathbb {Q}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-Gorenstein case.</p>
Autoren
  • Manuel Blickle
DOI
10.1090/s1056-3911-2012-00576-1
eISSN
1534-7486
ISSN
1056-3911
Ausgabe der Veröffentlichung
1
Zeitschrift
Journal of Algebraic Geometry
Sprache
en
Online publication date
2012
Paginierung
49 - 83
Status
Published online
Herausgeber
American Mathematical Society (AMS)
Herausgeber URL
http://dx.doi.org/10.1090/s1056-3911-2012-00576-1
Datum der Datenerfassung
2021
Titel
Test ideals via algebras of 𝑝^{-𝑒}-linear maps
Ausgabe der Zeitschrift
22

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