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Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



Compactification of Drinfeld moduli spaces as moduli spaces of $A$-reciprocal maps and consequences for Drinfeld modular forms

Author: Richard Pink
Journal: J. Algebraic Geom. 30 (2021), 477-527
Published electronically: December 17, 2020
MathSciNet review: 4283550
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Abstract | References | Additional Information

Abstract: 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 where $A=\mathbb {F}_q[t]$ 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 similar results in general, but the proof will require more ideas.

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Additional Information

Richard Pink
Affiliation: Department of Mathematics, ETH Zürich, 8092 Zürich, Switzerland
MR Author ID: 139765

Received by editor(s): March 7, 2019
Received by editor(s) in revised form: January 30, 2020, and May 14, 2020
Published electronically: December 17, 2020
Dedicated: In memory of David Goss
Article copyright: © Copyright 2020 University Press, Inc.