A Weil-Barsotti formula for Drinfeld modules

Lehmer Inequality and the Mordell-Weil Theorem for Drinfeld modules

In this paper we prove a special case of the Lehmer inequality for Drinfeld modules. Also, based on this inequality, we prove certain Mordell-Weil type of theorems for certain infinitely generated fields.

Drinfeld modular curve and Weil pairing

In this paper we describe the compactification of the Drinfeld modular curve. This compactification is analogous to the compactification of the classical modular curve given by Katz and Mazur. We show how the Weil pairing on Drinfeld modules that we defined in earlier work gives rise to a map on the Drinfeld modular curve. We introduce the Tate-Drinfeld module and show how this describes the formal neighbourhood of the scheme of cusps of the Drinfeld modular curve.

阿贝尔概型的扩张与加法群

Extensions of Abelian Schemes and the Additive Group

研究通过乘法群在 fppf 拓扑中计算阿贝尔概型和加法群的扩张层，给出巴尔索蒂 - 韦伊公式广义简化证明、特定\(\underline{\operatorname{Ext}}\)群结果，为相关理论提供新结论。

On ring class eigenspaces of Mordell-Weil groups of elliptic curves over global function fields

If E is a non-isotrivial elliptic curve over a global function field F of odd characteristic we show that certain Mordell-Weil groups of E have 1-dimensional eigenspace relative to a fixed complex ring class character provided that the projection onto this eigenspace of a suitable Drinfeld-Heegner point is nonzero. This represents the analogue in the function field setting of a theorem for rational elliptic curves due to Bertolini and Darmon, and at the same time is a generalization of the main result proved by Brown in his monograph on Heegner modules. As in the number field case, our proof e…

通过Szegő核实现有限剩余卡西米尔与Weil算子的几何化

Geometric Realization of Finite Residue Casimirs and Weil Operators via Szegő Kernels

本文针对有限域上带无穷远点的光滑射影曲线，通过Szegő核实现有限剩余卡西米尔与Weil算子的几何化，为相关配对研究提供了几何基础。

A chiral Borel-Weil-Bott theorem

We compute the cohomology of modules over the algebra of twisted chiral differential operators over the flag manifold. This is applied to (1) finding the character of $G$-integrable irreducible highest weight modules over the affine Lie algebra at the critical level, and (2) computing a certain elliptic genus of the flag manifold. The main tool is a result that interprets the Drinfeld-Sokolov reduction as a derived functor.