Categorical traces and a relative Lefschetz-Verdier formula

Autor:	Lu, Qing, Zheng, Weizhe
Rok vydání:	2020
Předmět:	Mathematics - Algebraic Geometry Mathematics - Category Theory 14F20 (Primary) 18M05 18N10 32S30 (Secondary)
Zdroj:	Forum Math. Sigma 10 (2022), e10
Druh dokumentu:	Working Paper
DOI:	10.1017/fms.2022.2
Popis:	We prove a relative Lefschetz-Verdier theorem for locally acyclic objects over a Noetherian base scheme. This is done by studying duals and traces in the symmetric monoidal $2$-category of cohomological correspondences. We show that local acyclicity is equivalent to dualizability and deduce that duality preserves local acyclicity. As another application of the category of cohomological correspondences, we show that the nearby cycle functor over a Henselian valuation ring preserves duals, generalizing a theorem of Gabber. Comment: 27 pages. v4: minor improvements. To appear in Forum of Mathematics, Sigma
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2005.08522 Zobrazit plný text záznamu View this record from Arxiv