Abstract
We construct a descent-of-scalars criterion for -linear abelian categories. Using advances in the Langlands correspondence due to Abe, we build a correspondence between certain rank 2 local systems and certain Barsotti–Tate groups on complete curves over a finite field. We conjecture that such Barsotti–Tate groups “come from” a family of fake elliptic curves. As an application of these ideas, we provide a criterion for being a Shimura curve over . Along the way we formulate a conjecture on the field-of-coefficients of certain compatible systems.
Citation
Raju Krishnamoorthy. "Rank 2 local systems, Barsotti–Tate groups, and Shimura curves." Algebra Number Theory 16 (2) 231 - 259, 2022. https://doi.org/10.2140/ant.2022.16.231
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