Flat quasi-coherent sheaves as directed colimits, and quasi-coherent cotorsion periodicity

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F24%3A00604957" target="_blank" >RIV/67985840:_____/24:00604957 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1007/s10468-024-10296-4" target="_blank" >https://doi.org/10.1007/s10468-024-10296-4</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s10468-024-10296-4" target="_blank" >10.1007/s10468-024-10296-4</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Flat quasi-coherent sheaves as directed colimits, and quasi-coherent cotorsion periodicity

Popis výsledku v původním jazyce

We show that every flat quasi-coherent sheaf on a quasi-compact quasi-separated scheme is a directed colimit of locally countably presentable flat quasi-coherent sheaves. More generally, the same assertion holds for any countably quasi-compact, countably quasi-separated scheme. Moreover, for three categories of complexes of flat quasi-coherent sheaves, we show that all complexes in the category can be obtained as directed colimits of complexes of locally countably presentable flat quasi-coherent sheaves from the same category. In particular, on a quasi-compact semi-separated scheme, every flat quasi-coherent sheaf is a directed colimit of flat quasi-coherent sheaves of finite projective dimension. In the second part of the paper, we discuss cotorsion periodicity in category-theoretic context, generalizing an argument of Bazzoni, Cortés-Izurdiaga, and Estrada. As the main application, we deduce the assertion that any cotorsion-periodic quasi-coherent sheaf on a quasi-compact semi-separated scheme is cotorsion.

Název v anglickém jazyce

Flat quasi-coherent sheaves as directed colimits, and quasi-coherent cotorsion periodicity

Popis výsledku anglicky

We show that every flat quasi-coherent sheaf on a quasi-compact quasi-separated scheme is a directed colimit of locally countably presentable flat quasi-coherent sheaves. More generally, the same assertion holds for any countably quasi-compact, countably quasi-separated scheme. Moreover, for three categories of complexes of flat quasi-coherent sheaves, we show that all complexes in the category can be obtained as directed colimits of complexes of locally countably presentable flat quasi-coherent sheaves from the same category. In particular, on a quasi-compact semi-separated scheme, every flat quasi-coherent sheaf is a directed colimit of flat quasi-coherent sheaves of finite projective dimension. In the second part of the paper, we discuss cotorsion periodicity in category-theoretic context, generalizing an argument of Bazzoni, Cortés-Izurdiaga, and Estrada. As the main application, we deduce the assertion that any cotorsion-periodic quasi-coherent sheaf on a quasi-compact semi-separated scheme is cotorsion.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA20-13778S" target="_blank" >GA20-13778S: Symetrie, duality a aproximace v derivované algebraické geometrii a teorii reprezentací</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2024

Kód důvěrnosti údajů

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

Název periodika

Algebras and Representation Theory

ISSN

1386-923X

e-ISSN

1572-9079

Svazek periodika

27

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

27

Strana od-do

2267-2293

Kód UT WoS článku

001371505800001

EID výsledku v databázi Scopus

2-s2.0-85211779250