Rank 2 local systems, Barsotti–Tate groups, and Shimura curves
R Krishnamoorthy - Algebra & Number Theory, 2022 - msp.org
Algebra & Number Theory, 2022•msp.org
We construct a descent-of-scalars criterion for K-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 𝔽 q.
Along the way we formulate a conjecture on the field-of-coefficients of certain compatible …
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 𝔽 q.
Along the way we formulate a conjecture on the field-of-coefficients of certain compatible …
Abstract
We construct a descent-of-scalars criterion for K-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 𝔽 q. Along the way we formulate a conjecture on the field-of-coefficients of certain compatible systems.
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