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The generic monodromy of Drinfeld modular varieties in special characteristic

· 2019 · math.NT · arXiv 1912.09820

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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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  • Higher Hida theory for Drinfeld modular curves math.NT · 2025-07-10 · conditional · none · ref 2 · internal anchor

    Higher Hida theory, including an interpolated Serre duality pairing, is constructed for Drinfeld modular curves.