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

Result code in 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>

Result on the web

<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>

Result language

angličtina

Original language name

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

Original language description

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.

Czech name

—

Czech description

—

Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10101 - Pure mathematics

Project

<a href="/en/project/GA20-13778S" target="_blank" >GA20-13778S: Symmetries, dualities and approximations in derived algebraic geometry and representation theory</a><br>

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2024

Confidentiality

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

Name of the periodical

Algebras and Representation Theory

ISSN

1386-923X

e-ISSN

1572-9079

Volume of the periodical

27

Issue of the periodical within the volume

6

Country of publishing house

NL - THE KINGDOM OF THE NETHERLANDS

Number of pages

27

Pages from-to

2267-2293

UT code for WoS article

001371505800001

EID of the result in the Scopus database

2-s2.0-85211779250