The pro-étale cohomology of Drinfeld's upper half space

On class number relations, intersections, and GL(2)-tale over the function field side

The aim of this paper is to study class number relations over function fields and the intersections of Hirzebruch-Zagier type divisors on the Drinfeld-Stuhler modular surfaces. The main bridge is a particular "harmonic" theta series with nebentypus. Using the strong approximation theorem, the Fourier coefficients of this series are expressed in two ways; one comes from modified Hurwitz class numbers and another gives the intersection numbers in question. An elaboration of this approach enables us to interpret these class numbers as a "mass sum" over the CM points on the Drinfeld-Stuhler modula…

Change of Coefficients for Drinfeld Modules, Shtuka, and Abelian Sheaves

We study the passage from Drinfeld-A'-modules to Drinfeld-A-modules for a given finite flat inclusion A \subset A'. We show that this defines a morphism from the moduli space of Drinfeld-A'-modules to the moduli space of Drinfeld-A-modules which is proper but in general not representable. For Drinfeld-Anderson shtuka and abelian sheaves instead of Drinfeld modules we obtain the same results.

Compactification of Drinfeld Moduli Spaces as Moduli Spaces of $A$-Reciprocal Maps and Consequences for Drinfeld Modular Forms

We construct a compactification of the moduli space of Drinfeld modules of rank $r$ and level $N$ as a moduli space of $A$-reciprocal maps. This is closely related to the Satake compactification, but not exactly the same. The construction involves some technical assumptions on $N$ that are satisfied for a cofinal set of ideals $N$. In the special case $A={\mathbb F}_q[t]$ and $N=(t^n)$ we obtain a presentation for the graded ideal of Drinfeld cusp forms of level $N$ and all weights and can deduce a dimension formula for the space of cusp forms of any weight. We expect the same results in gener…

Drinfeld Shtuka模空间的水平映射的紧化

Compactification of Level Maps of Moduli Spaces of Drinfeld Shtukas

本文定义任意秩Drinfeld shtuka的Drinfeld水平结构，证明其模空间正则且存在有限平坦水平映射，并证明其提供了朴素水平结构模空间的良好整模型与相对紧化。

关于德林费尔德可代表性定理

On Drinfeld's representability theorem

本文提供德林费尔德可代表性定理的新证明，并详细阐述其模空间与p-adic对称空间的正式模型。

Automorphisms of Products of Drinfeld Half Planes

The Drinfeld upper half-planes play the role of symmetric spaces in the $p$-adic analytic world. We find the automorphism group of a product of such spaces, where each may be defined over a different field. We deduce a rigidity theorem for quotients of such products by discrete and torsion free groups.