Generalized hypergeometric equations and $2$d TQFT for dormant opers in characteristic $\leq 7$

Keita Mori; Yasuhiro Wakabayashi

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arXiv · 2509.03994

Generalized hypergeometric equations and $2$d TQFT for dormant opers in characteristic $\leq 7$

Keita Mori·Yasuhiro Wakabayashi

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Abstract

This note studies $\mathrm{PGL}_n$-opers arising from generalized hypergeometric differential equations in prime characteristic $p$. We prove that these opers are rigid within the class of dormant opers. By combining this rigidity result with previous work in the enumerative geometry of dormant opers, we obtain a complete and explicit description of the $2$d TQFTs that compute the number of dormant $\mathrm{PGL}_n$-opers for primes $p \leq 7$.

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Keita Mori, Yasuhiro Wakabayashi. 2025-09-04. Generalized hypergeometric equations and $2$d TQFT for dormant opers in characteristic $\leq 7$. https://arxiv.org/abs/2509.03994

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