Plectic structures in p-adic de Rham cohomology

Loeffler, David; Zerbes, Sarah Livia

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Journal article

Plectic structures in p-adic de Rham cohomology

Loeffler, David ORCID UniDistance Suisse
Zerbes, Sarah Livia ORCID ETH Zurich

2023

Published in:

Journal of Number Theory. - accepted, in press. - 2023

English 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 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 étale cohomology. We prove this conjecture in the case [F:Q] =2 under some mild assumptions; and for general F we prove a weaker statement which is strong evidence for the conjecture, showing that the plectic Hodge filtration has a canonical splitting given by intersecting with simultaneous eigenspaces for the partial Frobenii.

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