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Rank 2 local systems, Barsotti–Tate groups, and Shimura curves
Algebra & Number Theory ( IF 0.9 ) Pub Date : 2022-04-27 , DOI: 10.2140/ant.2022.16.231
Raju Krishnamoorthy

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 𝔽q. Along the way we formulate a conjecture on the field-of-coefficients of certain compatible systems.



中文翻译:

Rank 2 局部系统、Barsotti-Tate 群和 Shimura 曲线

我们构建了一个标量下降标准ķ- 线性阿贝尔范畴。使用由于 Abe 导致的 Langlands 对应关系的进步,我们在有限域上的完整曲线上建立了某些 2 级局部系统和某些 Barsotti-Tate 群之间的对应关系。我们推测这样的 Barsotti-Tate 群“来自”一个假椭圆曲线族。作为这些想法的应用,我们提供了一个标准𝔽q. 在此过程中,我们对某些兼容系统的系数场进行了猜想。

更新日期:2022-04-27
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