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arXiv · 2012.08585

On certain cohomology groups attached to $\mathfrak{p}^{\infty}$-towers of quaternionic Hilbert modular varieties

Michael Spieß
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Abstract

For a totally real number field $F$ and a nonarchimedean prime $\mathfrak{p}$ of $F$ lying above a prime number $p$ we introduce certain sheaf cohomology groups that intertwine the $\mathfrak{p}^{\infty}$-tower of a quaternionic Hilbert modular variety associated to a quaternion algebra $D$ over $F$ that is split at $\mathfrak{p}$ and a $p$-adically admissible representation of $\mbox{PGL}_2(F_{\mathfrak{p}})$. Applied to infinitesimal $p$-adic deformations of the local factor at $\mathfrak{p}$ of a cuspidal automorphic representation $\pi$ of $D^*(\mathbb{A})$ this yields a natural construction of infinitesimal deformations of the Galois representation attached to $\pi$.

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Michael Spieß. 2020-12-15. On certain cohomology groups attached to $\mathfrak{p}^{\infty}$-towers of quaternionic Hilbert modular varieties. https://arxiv.org/abs/2012.08585

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