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arXiv · 2611.07849

A Hypergeometric RM Surface: Integral Monodromy and Level-11 Covers

Devendra Tiwari
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Abstract

We study a genus-two hypergeometric family whose Jacobians have real multiplication by $\Q(\sqrt5)$. We identify the relevant primitive factor and integral rank-two monodromy; at one real embedding the projective image is $Δ(2,5,\infty)$, while the conjugate image is nondiscrete. At the primes above $11$, the degree-$12$ Borel covers are quadratic pullbacks of genus-one triangular modular curves. The same rank-two systems have finite-field hypergeometric Frobenius traces, yielding the local Euler factors and a quadratic transformation twisted by the character of $2$.

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Devendra Tiwari. 2026-11-05. A Hypergeometric RM Surface: Integral Monodromy and Level-11 Covers. https://arxiv.org/abs/2611.07849

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