Loeffler, David Zerbes, Sarah Livia 2023 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. application/pdf https://sonar.unidistance.ch/global/documents/326706 https://n2t.net/ark:/51647/srd1326706 https://sonar.unidistance.ch/documents/326706/files/plectic.pdf eng https://arxiv.org/abs/2211.12078 info:eu-repo/semantics/altIdentifier/ark/51647/srd1326706 info:eu-repo/semantics/openAccess CC BY Journal of Number Theory. - accepted, in press. - 2023 info:eu-repo/classification/udc/51 Plectic structures in p-adic de Rham cohomology http://purl.org/coar/resource_type/c_6501