Showing papers by "Valery A. Lunts published in 2017"
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TL;DR: In this paper, the authors compare the categorical measure of the corresponding quotient stack and the extended quotient of a variety with a finite group action and show that for a wide range of cases, these two measures coincide.
Abstract: Given a variety with a finite group action, we compare its equivariant categorical measure, that is, the categorical measure of the corresponding quotient stack, and the categorical measure of the extended quotient. Using weak factorization for orbifolds, we show that for a wide range of cases, these two measures coincide. This implies, in particular, a conjecture of Galkin and Shinder on categorical and motivic zeta-functions of varieties. We provide examples showing that, in general, these two measures are not equal. We also give an example related to a conjecture of Polishchuk and Van den Bergh, showing that a certain condition in this conjecture is indeed necessary.
7 citations
TL;DR: In this paper, it was shown that the category D^b(coh X) contains no proper full triangulated subcategories which are regular, and also bound from below the dimension of a regular category $T$ if there exists a triangulation functor from T \ to D √ coh X with certain properties.
Abstract: Let $R$ be a commutative Noetherian ring such that $X=Spec R$ is connected. We prove that the category $D^b(coh X)$ contains no proper full triangulated subcategories which are regular. We also bound from below the dimension of a regular category $T$, if there exists a triangulated functor $T \to D^b(coh X)$ with certain properties. Applications are given to cohomological annihilator of $R$ and to point-like objects in $T$.
2 citations