Toroidal compactifications of the moduli spaces of Drinfeld modules

Takako Fukaya; Kazuya Kato; Romyar Sharifi

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arXiv · 2008.13376

Toroidal compactifications of the moduli spaces of Drinfeld modules

Takako Fukaya·Kazuya Kato·Romyar Sharifi

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Abstract

We construct toroidal compactifications of the moduli spaces of Drinfeld $\mathbb{F}_q[T]$-modules of rank $d$ with level $N$ structure as moduli spaces of log Drinfeld modules of rank $d$ with level $N$ structure. The toroidal compactifications are log regular schemes associated to rational cone decompositions, and there are regular ones among them. To construct these toroidal compactifications, we blow up the Satake compactification of Pink and employ the theory of formal moduli and a process of iterated Tate uniformization.

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Takako Fukaya, Kazuya Kato, Romyar Sharifi. 2020-08-31. Toroidal compactifications of the moduli spaces of Drinfeld modules. https://arxiv.org/abs/2008.13376

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