On certain cohomology groups attached to \(\mathfrak{p}^{\infty}\)-towers of quaternionic Hilbert modular varieties
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 \(...
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Published in | arXiv.org |
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Main Author | |
Format | Paper |
Language | English |
Published |
Ithaca
Cornell University Library, arXiv.org
15.12.2020
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Subjects | |
Online Access | Get full text |
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Summary: | 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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ISSN: | 2331-8422 |