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arXiv · 2503.10524

On the computation of the vanishing locus of a finitely presented functor

Sebastian Posur
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Abstract

We discuss invariants which are helpful for the computation of the vanishing locus of a finitely presented functor $\mathcal{G}$, i.e., the set of points in the Ziegler spectrum on which $\mathcal{G}$ vanishes. These invariants are: the rank of $\mathcal{G}$, the supports of its co- and contravariant defect, and the class of $\mathcal{G}$ in the Grothendieck group of the category of finitely presented functors. We show that these invariants determine the vanishing locus in the case of a finitely presented functor over a Dedekind domain.

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Sebastian Posur. 2025-03-13. On the computation of the vanishing locus of a finitely presented functor. https://arxiv.org/abs/2503.10524

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