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Mathematics > Algebraic Geometry

arXiv:1812.10890 (math)
[Submitted on 28 Dec 2018 (v1), last revised 24 Oct 2021 (this version, v4)]

Title:Gysin triangles in the category of motifs with modulus

Authors:Keiho Matsumoto
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Abstract:In this paper, we study a Gysin triangle in the category of motives with modulus. 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. The corollary implies that an object in the category of motives with modulus 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.
Subjects: Algebraic Geometry (math.AG)
MSC classes: 19E15
Cite as: arXiv:1812.10890 [math.AG]
  (or arXiv:1812.10890v4 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.1812.10890
Related DOI: https://doi.org/10.1017/S1474748021000554

Submission history

From: Keiho Matsumoto [view email]
[v1] Fri, 28 Dec 2018 04:33:28 UTC (11 KB)
[v2] Sun, 22 Mar 2020 12:06:41 UTC (1 KB) (withdrawn)
[v3] Wed, 7 Oct 2020 12:18:00 UTC (135 KB)
[v4] Sun, 24 Oct 2021 14:17:12 UTC (31 KB)
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