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arXiv:2311.12254 [math.AG]AbstractReferencesReviewsResources

A Counterexample to a Question on Grothendieck Groups of Schemes

Amal Mattoo

Published 2023-11-21Version 1

If an element of the Grothendieck group of the derived category of a scheme is locally represented by perfect complexes, then can the original element be represented by a perfect complex? We provide a counterexample on a projective variety of dimension 2, as well as a counterexample on a thickening of a Dedekind domain.

Comments: 7 pages
Categories: math.AG
Subjects: 14F08, 19A99, 13D15
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