Plectic structures in p-adic de Rham cohomology
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2025-05
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Journal Article
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yes
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Abstract
Given a Hilbert modular form for a totally real field $F$, and a prime $p$ split completely in $F$, the $f$-eigenspace in $p$-adic de Rham cohomology of the Hilbert modular variety has a family of partial filtrations and partial Frobenius maps, indexed by the primes of $F$ above $p$. The general plectic conjectures of Nekovar and Scholl suggest a "plectic comparison isomorphism" comparing these structures to etale cohomology. We prove this conjecture in the case $[F : \mathbf{Q}] = 2$ under some mild assumptions; and for general $F$ we prove a weaker statement which is strong evidence for the conjecture, showing that plectic Hodge filtration has a canonical splitting given by intersecting with simultaneous eigenspaces for the partial Frobenii. (In memory of Jan Nekovar)
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published
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270
Pages / Article No.
238 - 259
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Elsevier
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Subject
Hilbert modular varieties; p-adic Hodge theory; Plectic conjectures; Higher Coleman theory
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09765 - Zerbes, Sarah / Zerbes, Sarah
00009 - ETH-nahe Einheiten
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Is new version of: 10.48550/arXiv.2211.12078