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June 2019 Artin Motives, Weights, and Motivic Nearby Sheaves
Florian Ivorra, Julien Sebag
Michigan Math. J. 68(2): 337-376 (June 2019). DOI: 10.1307/mmj/1551258026

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).

Citation

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Florian Ivorra. Julien Sebag. "Artin Motives, Weights, and Motivic Nearby Sheaves." Michigan Math. J. 68 (2) 337 - 376, June 2019. https://doi.org/10.1307/mmj/1551258026

Information

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

zbMATH: 07084766
MathSciNet: MR3961220
Digital Object Identifier: 10.1307/mmj/1551258026

Subjects:
Primary: 14B20, 14C15, 14F42, 14G22, 32S30

Rights: Copyright © 2019 The University of Michigan

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Vol.68 • No. 2 • June 2019
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