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Functoriality of motivic lifts of the canonical construction

Torzewski, A; (2019) Functoriality of motivic lifts of the canonical construction. manuscripta mathematica 10.1007/s00229-019-01150-9. (In press). Green open access

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Abstract

Let (G,X) be a Shimura datum and K a neat open compact subgroup of $G(\mathbb{A}_f)$. Under mild hypothesis on (G,X), the canonical construction associates a variation of Hodge structure on $\textrm{Sh}_K(G,X)(\mathbb{C})$ to a representation of G. It is conjectured that this should be of motivic origin. Specifically, there should be a lift of the canonical construction which takes values in relative Chow motives over $\textrm{Sh}_K(G,X)$ and is functorial in (G,X). Using the formalism of mixed Shimura varieties, we show that such a motivic lift exists on the full subcategory of representations of Hodge type {(-1,0),(0,-1)}. If (G,X) is equipped with a choice of PEL-datum, Ancona has defined a motivic lift for all representations of G. We show that this is independent of the choice of PEL-datum and give criteria for it to be compatible with base change.

Type: Article
Title: Functoriality of motivic lifts of the canonical construction
Open access status: An open access version is available from UCL Discovery
DOI: 10.1007/s00229-019-01150-9
Publisher version: http://dx.doi.org/10.1007/s00229-019-01150-9
Language: English
Additional information: Copyright information © The Author(s) 2019 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
URI: https://discovery-pp.ucl.ac.uk/id/eprint/10082847
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