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Barsotti–Tate groups and p-adic representations of the fundamental group scheme

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Abstract

On a scheme S over a base scheme B we study the category of locally constant BT groups, i.e. groups over S that are twists, in the flat topology, of BT groups defined over B. These groups generalize p-adic local systems and can be interpreted as integral p-adic representations of the fundamental group scheme of S/B (classifying finite flat torsors on the base scheme) when such a group exists. We generalize to these coefficients the Katz correspondence for p-adic local systems and show that they are closely related to the maximal nilpotent quotient of the fundamental group scheme.

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Authors and Affiliations

  1. Dipartimento di Matematica Pura ed Applicata, Università degli Studi di Padova, Via Trieste 63, 35121, Padova, Italy

    Marco A. Garuti

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  1. Marco A. Garuti
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Correspondence to Marco A. Garuti.

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Garuti, M.A. Barsotti–Tate groups and p-adic representations of the fundamental group scheme. Math. Ann. 341, 603–622 (2008). https://doi.org/10.1007/s00208-007-0205-0

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