Purity, ascent and periodicity for Gorenstein flat cotorsion modules

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F25%3A10505576" target="_blank" >RIV/00216208:11320/25:10505576 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=b87jOBR.gW" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=b87jOBR.gW</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1112/jlms.70201" target="_blank" >10.1112/jlms.70201</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Purity, ascent and periodicity for Gorenstein flat cotorsion modules

Popis výsledku v původním jazyce

We investigate purity within the Frobenius category of Gorenstein flat cotorsion modules, which can be seen as an infinitely generated analogue of the Frobenius category of Gorenstein projective objects. As such, the associated stable category can be viewed as an alternative approach to a big singularity category, which is equivalent to Krause&apos;s when the ring is Gorenstein. We study the pure structure of the stable category, and show that it is fundamentally related to the pure structure of the Gorenstein flat modules. Following that, we give conditions for extension of scalars to preserve Gorenstein flat cotorsion modules. In this case, one obtains an induced triangulated functor on the stable categories. We show that under mild conditions that these functors preserve the pure structure, both on the triangulated and module category level. Along the way, we consider particular phenomena over commutative rings, the cumulation of which is an extension of Kn &amp; ouml;rrer periodicity, giving a triangulated equivalence between Krause&apos;s big singularity categories for a complete hypersurface singularity and its twofold double-branched cover.

Název v anglickém jazyce

Purity, ascent and periodicity for Gorenstein flat cotorsion modules

Popis výsledku anglicky

We investigate purity within the Frobenius category of Gorenstein flat cotorsion modules, which can be seen as an infinitely generated analogue of the Frobenius category of Gorenstein projective objects. As such, the associated stable category can be viewed as an alternative approach to a big singularity category, which is equivalent to Krause&apos;s when the ring is Gorenstein. We study the pure structure of the stable category, and show that it is fundamentally related to the pure structure of the Gorenstein flat modules. Following that, we give conditions for extension of scalars to preserve Gorenstein flat cotorsion modules. In this case, one obtains an induced triangulated functor on the stable categories. We show that under mild conditions that these functors preserve the pure structure, both on the triangulated and module category level. Along the way, we consider particular phenomena over commutative rings, the cumulation of which is an extension of Kn &amp; ouml;rrer periodicity, giving a triangulated equivalence between Krause&apos;s big singularity categories for a complete hypersurface singularity and its twofold double-branched cover.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GJ20-02760Y" target="_blank" >GJ20-02760Y: Cohen-Macaulayovy okruhy a jejich aplikace ve vyšší algebře a topologii</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2025

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of the London Mathematical Society

ISSN

0024-6107

e-ISSN

1469-7750

Svazek periodika

111

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

47

Strana od-do

e70201

Kód UT WoS článku

001514043300030

EID výsledku v databázi Scopus

2-s2.0-105008305400