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GYSIN TRIANGLES IN THE CATEGORY OF MOTIFS WITH MODULUS

Part of: Cycles and subschemes

Published online by Cambridge University Press:  06 January 2022

Keiho Matsumoto Open the ORCID record for Keiho Matsumoto [Opens in a new window]
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Abstract

In this article, we study a Gysin triangle in the category of motives with modulus (Theorem 1.2). We can understand this Gysin triangle as a motivic lift of the Gysin triangle of log-crystalline cohomology due to Nakkajima and Shiho. After that we compare motives with modulus and Voevodsky motives (Corollary 1.6). The corollary implies that an object in $\operatorname {\mathbf {MDM}^{\operatorname {eff}}}$ decomposes into a p-torsion part and a Voevodsky motive part. We can understand the corollary as a motivic analogue of the relationship between rigid cohomology and log-crystalline cohomology.

Keywords

Chow groupmotives

MSC classification

Primary: 14C15: (Equivariant) Chow groups and rings; motives
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 22 , Issue 5 , September 2023 , pp. 2131 - 2154
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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