A Counterexample to a Question on Grothendieck Groups of Schemes

2023/11/21 by Amal Mattoo, Mattoo, Amal
Mathematics · #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #Algebraic structures and combinatorial models

paper · pdf · doi:10.48550/arxiv.2311.12254

Abstract

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.

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