Integral canonical models for automorphic vector bundles of abelian type

Lovering, Tom

doi:10.2140/ant.2017.11.1837

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Integral canonical models for automorphic vector bundles of abelian type

Tom Lovering

Vol. 11 (2017), No. 8, 1837–1890

DOI: 10.2140/ant.2017.11.1837

Abstract

We define and construct integral canonical models for automorphic vector bundles over Shimura varieties of abelian type.

More precisely, we first build on Kisin’s work to construct integral canonical models over $O_{E} [1 ∕ N]$ for Shimura varieties of abelian type with hyperspecial level at all primes not dividing $N$ compatible with Kisin’s construction. We then define a notion of an integral canonical model for the standard principal bundles lying over Shimura varieties and proceed to construct them in the abelian type case. With these in hand, one immediately also gets integral models for automorphic vector bundles.

Keywords

Shimura varieties, automorphic vector bundles, integral models, Shimura, abelian type

Mathematical Subject Classification 2010

Primary: 11G18

Secondary: 14G35

Milestones

Received: 29 August 2016

Revised: 8 June 2017

Accepted: 21 July 2017

Published: 15 October 2017

Authors

Tom Lovering
Department of Mathematics Harvard University 1 Oxford St. Cambridge, MA 02138 United States

Vol. 11, No. 8, 2017