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Ranks of Verdier quotients of derived categories over local rings
Abstract
Let R be a commutative noetherian local ring with residue field k. Denote by Db(R) the bounded derived category of finitely generated R-modules. In this paper, we introduce the notion of ranks of triangulated categories and study Verdier quotients of Db(R) from the viewpoint of this invariant. Our main result determines the rank of the Verdier quotient Db(R)/thick(R⊕ k) in terms of the ranks of the categories of maximal Cohen-Macaulay modules on the punctured spectrum.
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BibTeX
@misc{dey2026ranks,
title = {{Ranks of Verdier quotients of derived categories over local rings}},
author = {Souvik Dey and Yuki Mifune},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.06456},
eprint = {2609.06456},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.06456},
}
RIS
TY - UNPB
TI - Ranks of Verdier quotients of derived categories over local rings
AU - Souvik Dey
AU - Yuki Mifune
PY - 2026
DA - 2026/09/06
PB - arXiv
DO - 10.48550/arxiv.2609.06456
UR - https://arxiv.org/abs/2609.06456
AB - Let R be a commutative noetherian local ring with residue field k. Denote by D^b(R) the bounded derived category of finitely generated R-modules. In this paper, we introduce the notion of ranks of triangulated categories and study Verdier quotients of D^b(R) from the viewpoint of this invariant. Our main result determines the rank of the Verdier quotient D^b(R)/thick(R⊕ k) in terms of the ranks of the categories of maximal Cohen-Macaulay modules on the punctured spectrum.
ER -