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arXiv · 1912.09820

The generic monodromy of Drinfeld modular varieties in special characteristic

Gebhard Böckle·Florian Breuer
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Abstract

By combining theorems of Drinfeld and Strauch, we show that the monodromy representation on the special fibre of a Drinfeld modular variety, with level not divisible by the characteristic, is surjective. We illustrate this result in the special case of Drinfeld $\mathbb{F}_q[t]$-modules in level $t$, and apply this to show that the Kronecker factors of a Drinfeld modular polynomial in rank $r$ are irreducible.

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Gebhard Böckle, Florian Breuer. 2019-12-20. The generic monodromy of Drinfeld modular varieties in special characteristic. https://arxiv.org/abs/1912.09820

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