The finite type of modules of bounded projective dimension and Serre's conditions

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F24%3A00588523" target="_blank" >RIV/67985840:_____/24:00588523 - isvavai.cz</a>
Alternative codes found
RIV/00216208:11320/24:10489442
Result on the web
<a href="https://doi.org/10.1112/blms.13099" target="_blank" >https://doi.org/10.1112/blms.13099</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1112/blms.13099" target="_blank" >10.1112/blms.13099</a>

Result language
angličtina
Original language name
The finite type of modules of bounded projective dimension and Serre's conditions
Original language description
Let (Formula presented.) be a commutative Noetherian ring. For a natural number (Formula presented.), we prove that the class of modules of projective dimension bounded by (Formula presented.) is of finite type if and only if (Formula presented.) satisfies Serre's condition (Formula presented.). In particular, this answers positively a question of Bazzoni and Herbera in the specific setting of a Gorenstein ring. Applying similar techniques, we also show that the (Formula presented.) -dimensional version of the Govorov–Lazard theorem holds if and only if (Formula presented.) satisfies the ‘almost’ Serre condition (Formula presented.).
Czech name
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Czech description
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Type
J<sub>imp</sub> - 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/GA23-05148S" target="_blank" >GA23-05148S: Homological and structural theory in geometric contexts</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

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