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Relative p-adic Hodge theory : foundations / Kiran S. Kedlaya; Ruochuan Liu

By: Contributor(s): Resource type: Ressourcentyp: BuchBookLanguage: English Series: Astérisque ; 371Publisher: Paris : Soc. Mathématique de France, 2015Description: 239 S. : graph. DarstISBN:
  • 9782856298077
Other title:
  • Parallelsacht.: Théorie de Hodge p-adique dans le cas relatif
Subject(s): Additional physical formats: Erscheint auch als: Relative p-adic Hodge theory. Online-Ausgabe Paris : Société Mathématique de France, 2015. 1 Online-Ressource (239 Seiten)MSC: MSC: 14-02 | 14F30 | 14G22 | 13F35 | 11S25RVK: RVK: SI 832LOC classification:
  • QA564
DOI: DOI: 10.24033/ast.957Summary: "We describe a new approach to relative p-adic Hodge theory based on systematic use of Witt vector constructions and nonarchimedean analytic geometry in the style of both Berkovich and Huber. We give a thorough development of [phi]-modules over a relative Robba ring associated to a perfect Banach ring of characteristic p, including the relationship between these objects and étale Z[subscript p]-local systems and Q[subscript p]-local systems on the algebraic and analytic spaces associated to the base ring, and the relationship between (pro-)étale cohomology and [phi]-cohomology. We also make a critical link to mixed characteristic by exhibiting an equivalence of tensor categories between the finite étale algebras over an arbitrary perfect Banach algebra over a nontrivially normed complete field of characteristic p and the finite étale algebras over a corresponding Banach Q[subscript p]-algebra. This recovers the homeomorphism between the absolute Galois groups of F[subscript p](([pi])) and Q[subscript p] ([mu] [subscript p][infinity]) given by the field of norms construction of Fontaine and Wintenberger, as well as generalizations considered by Andreatta, Brinon, Faltings, Gabber, Ramero, Scholl, and most recently Scholze. Using Huber's formalism of adic spaces and Scholze's formalism of perfectoid spaces, we globalize the constructions to give several descriptions of the étale local systems on analytic spaces over p-adic fields. One of these descriptions uses a relative version of the Fargues-Fontaine curvePPN: PPN: 829645853
Holdings
Item type Home library Shelving location Call number Status Barcode
Freihandbestand ausleihbar Fachbibliothek Mathematik Bibliothek / frei aufgestellt Z 533-371.2015 Available 36389788090
Total holds: 0
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