The Michigan Mathematical Journal

Artin Motives, Weights, and Motivic Nearby Sheaves

Florian Ivorra and Julien Sebag

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Abstract

In this paper, we compute the Artin part of a relative cohomological motive, introduced by Ayoub and Zucker, as a “weight zero part” in two challenging contexts. For this, we first introduce, in a very natural way, the part of punctual weight 0 of any complex of mixed Hodge modules and verify that the Hodge realization of the Artin part of smooth cohomological motives coincide with the part of punctual weight 0 of its realization. Second, we compute the Artin part of the motivic nearby sheaf, introduced by Ayoub, and relate it to the Betti cohomology of Berkovich spaces defined by tubes in non-Archimedean geometry. In particular, the former result provides a motivic interpretation of the Betti cohomology of the analytic Milnor fiber (seen as a Berkovich space).

Article information

Source
Michigan Math. J., Volume 68, Issue 2 (2019), 337-376.

Dates
Received: 30 May 2017
Revised: 23 July 2018
First available in Project Euclid: 27 February 2019

Permanent link to this document
https://projecteuclid.org/euclid.mmj/1551258026

Digital Object Identifier
doi:10.1307/mmj/1551258026

Mathematical Reviews number (MathSciNet)
MR3961220

Zentralblatt MATH identifier
07084766

Subjects
Primary: 14B20: Formal neighborhoods 14C15: (Equivariant) Chow groups and rings; motives 14F42: Motivic cohomology; motivic homotopy theory [See also 19E15] 14G22: Rigid analytic geometry 32S30: Deformations of singularities; vanishing cycles [See also 14B07]

Citation

Ivorra, Florian; Sebag, Julien. Artin Motives, Weights, and Motivic Nearby Sheaves. Michigan Math. J. 68 (2019), no. 2, 337--376. doi:10.1307/mmj/1551258026. https://projecteuclid.org/euclid.mmj/1551258026


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