{"id":{"repo_id":"cambridge","oai_identifier":"oai:www.repository.cam.ac.uk:1810/389514"},"canonical_url":"https://search.dev.ndltd.org/etd/cambridge/oai:www.repository.cam.ac.uk:1810/389514","repository":{"repo_id":"cambridge","name":"Cambridge University","base_url":"https://api.repository.cam.ac.uk/server/oai/request"},"display":{"title":"Equivariance in Tannakian duality and plectic p-adic Hodge theory","abstract":"For a gerbe G and a finite constant group S acting on it, we use the Grothendieck construction to define a semidirect product gerbe G ⋊ S. We describe such gerbes in terms of Cech cocycles via the cohomology of crossed modules. We characterise a dual form of the Grothendieck construction and show that in the special case of the group S acting on a Tannakian category C, it gives rise to the category C^S of S-equivariant objects of C. If G and C correspond by Tannakian duality, then so do G ⋊ S and C^S. We derive descent for Tannakian categories from a classification of Galois gerbes and give a criterion for a descended category to be neutral. We then study a plectic variant of Fontaine theory for p-adic representations of the local plectic Galois group at p associated to a totally real number field F, when p is inert in F. In particular, we show that the plectic crystalline Fontaine functor is valued in a category of plectic isocrystals. We prove that this category is Tannakian using the theory developed in the first part.","abstract_html":"For a gerbe G and a finite constant group S acting on it, we use the Grothendieck construction to define a semidirect product gerbe G ⋊ S. We describe such gerbes in terms of Cech cocycles via the cohomology of crossed modules. We characterise a dual form of the Grothendieck construction and show that in the special case of the group S acting on a Tannakian category C, it gives rise to the category C^S of S-equivariant objects of C. If G and C correspond by Tannakian duality, then so do G ⋊ S and C^S. We derive descent for Tannakian categories from a classification of Galois gerbes and give a criterion for a descended category to be neutral. We then study a plectic variant of Fontaine theory for p-adic representations of the local plectic Galois group at p associated to a totally real number field F, when p is inert in F. In particular, we show that the plectic crystalline Fontaine functor is valued in a category of plectic isocrystals. We prove that this category is Tannakian using the theory developed in the first part.","abstract_has_math":false,"creators":["Kofler, Lukas"],"institution":"University of Cambridge","degree_name":"Doctor of Philosophy (PhD)","degree_level":"Doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Scholl, Anthony"],"committee_chairs":[],"committee_members":[],"year":2025,"date_issued":"2025-03-21","date_published":"2025-03-21","updated_at":"2026-07-22T22:24:08Z","subjects":["Algebraic number theory","Mathematics","p-adic Hodge theory","Tannakian duality"],"languages":["eng"],"rights":[],"rights_urls":["https://www.repository.cam.ac.uk/bitstreams/8fb52048-6d7a-43c9-a4f7-a2da7dce877a/download","http://purl.org/NET/rdflicense/allrightsreserved"],"identifier_entries":[]},"links":{"outbound_url":"https://doi.org/10.17863/CAM.121373","outbound_label":"DOI","outbound_source":"dc:identifier.doi"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Scholl, Anthony"]},{"key":"dc:contributor.sponsor","label":"Sponsor","values":["Metheringham Scholarship"]},{"key":"dc:creator","label":"Author","values":["Kofler, Lukas"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.issued","label":"Date","values":["2025-03-21"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of Cambridge"]},{"key":"dc:relation.isreferencedby.uri","label":"Dc Relation Isreferencedby URI","values":["https://www.repository.cam.ac.uk/handle/1810/389514"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["Doctoral"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["Doctor of Philosophy (PhD)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Algebraic number theory","Mathematics","p-adic Hodge theory","Tannakian duality"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["https://www.repository.cam.ac.uk/bitstreams/8fb52048-6d7a-43c9-a4f7-a2da7dce877a/download","http://purl.org/NET/rdflicense/allrightsreserved"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.doi","label":"DOI","values":["https://doi.org/10.17863/CAM.121373"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://www.repository.cam.ac.uk/bitstreams/20e23853-078c-4f51-adc7-b188c7ef8657/download"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["For a gerbe G and a finite constant group S acting on it, we use the Grothendieck construction to define a semidirect product gerbe G ⋊ S. We describe such gerbes in terms of Cech cocycles via the cohomology of crossed modules. We characterise a dual form of the Grothendieck construction and show that in the special case of the group S acting on a Tannakian category C, it gives rise to the category C^S of S-equivariant objects of C. If G and C correspond by Tannakian duality, then so do G ⋊ S and C^S. We derive descent for Tannakian categories from a classification of Galois gerbes and give a criterion for a descended category to be neutral. We then study a plectic variant of Fontaine theory for p-adic representations of the local plectic Galois group at p associated to a totally real number field F, when p is inert in F. In particular, we show that the plectic crystalline Fontaine functor is valued in a category of plectic isocrystals. We prove that this category is Tannakian using the theory developed in the first part."]},{"key":"dc:format.checksum.md5","label":"Dc Format Checksum Md5","values":["57e861d612a9b9237679aa7d3ac9cb32","87eda9de84448d1f82354d60eee3eb5f"]},{"key":"dc:title","label":"Title","values":["Equivariance in Tannakian duality and plectic p-adic Hodge theory"]}]}],"canonical_facts":{"dc:contributor.advisor":["Scholl, Anthony"],"dc:contributor.sponsor":["Metheringham Scholarship"],"dc:creator":["Kofler, Lukas"],"dc:date.issued":["2025-03-21"],"dc:description.abstract":["For a gerbe G and a finite constant group S acting on it, we use the Grothendieck construction to define a semidirect product gerbe G ⋊ S. We describe such gerbes in terms of Cech cocycles via the cohomology of crossed modules. We characterise a dual form of the Grothendieck construction and show that in the special case of the group S acting on a Tannakian category C, it gives rise to the category C^S of S-equivariant objects of C. If G and C correspond by Tannakian duality, then so do G ⋊ S and C^S. We derive descent for Tannakian categories from a classification of Galois gerbes and give a criterion for a descended category to be neutral. We then study a plectic variant of Fontaine theory for p-adic representations of the local plectic Galois group at p associated to a totally real number field F, when p is inert in F. In particular, we show that the plectic crystalline Fontaine functor is valued in a category of plectic isocrystals. 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