Toward Shimurian analogs of Barsotti-Tate groups

Vladimir Drinfeld

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arXiv · 2309.02346

Toward Shimurian analogs of Barsotti-Tate groups

Vladimir Drinfeld

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Abstract

We first recall Grothendieck's notion of n-truncated Barsotti-Tate group. Such groups form an algebraic stack over the integers. The problem is to give an illuminating description of its reductions modulo powers of p. A related problem is to construct analogs of these reductions related to general Shimura varieties with good reduction at p. We discuss some conjectures on this subject based on the theory of prismatic cohomology.

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Vladimir Drinfeld. 2023-09-05. Toward Shimurian analogs of Barsotti-Tate groups. https://arxiv.org/abs/2309.02346

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