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003 OCoLC;

005 20151103143444.0;

008 150703t20152015fr a b 000 0 eng d;

020 a| 9782856298077q| (pbk.);

020 a| 2856298079q| (pbk.);

029 1 a| NLGGCb| 394348591;

035 a| (Sirsi) o913077122;

035 a| (OCoLC)913077122;

041 0 a| engb| engb| fre;

049 a| EREE;

050 4 a| QA564b| .K43 2015;

100 1 a| Kedlaya, Kiran Sridhara,d| 1974-e| author.=| ^A1270561;

245 10 a| Relative p-adic Hodge theory :b| foundations /c| Kiran S. Kedlaya, Ruochuan Liu.;

264 1 a| Paris :b| Société mathématique de France,c| 2015.;

300 a| 239 pages :b| illustrations ;c| 24 cm.;

336 a| textb| txt2| rdacontent;

337 a| unmediatedb| n2| rdamedia;

338 a| volumeb| nc2| rdacarrier;

490 1 a| Astérisque,x| 0303-1179 ;v| 371;

504 a| Includes bibliographical references (pages 231-239).;

520 3 a| "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 curve.";

546 a| Abstract also in French.;

650 0 a| Hodge theory.=| ^A145525;

650 0 a| p-adic fields.=| ^A237693;

650 0 a| Geometry, Algebraic.=| ^A42380;

700 1 a| Liu, Ruochuan,e| author.=| ^A1272171;

830 0 a| Astérisquev| 371.=| ^A682305;

938 a| YBP Library Servicesb| YANKn| 12521929;

938 a| Baker and Taylorb| BTCPn| BK0017435001;

949 a| QA564 .K43 2015h| Joyner48i| 30372016735273o| jwjh;

994 a| C0b| ERE;

596 a| 1;

998 a| 3793915;

999 a| QA564 .K43 2015w| LCc| 1i| 30372016735273d| 8/11/2015e| 8/11/2015l| JGESm| JOYNERr| Ys| Yt| JGESBKu| 8/11/2015x| BOOKz| JSTACKSo| .STAFF. jwjh;

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

Author/creator	Kedlaya, Kiran Sridhara, 1974- author.
Other author	Liu, Ruochuan, author.
Format	Book
Publication	Paris : Société mathématique de France, 2015.
Copyright Date	©2015
Description	239 pages : illustrations ; 24 cm.
Subjects	Hodge theory. p-adic fields. Geometry, Algebraic.

Series	Astérisque, 0303-1179 ; 371 Astérisque 371. ^A682305
Summary	"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 curve."
Bibliography note	Includes bibliographical references (pages 231-239).
Language	Abstract also in French.
ISBN	9782856298077 (pbk.)
ISBN	2856298079 (pbk.)

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Joyner	General Stacks	QA564 .K43 2015	✔ Available	Place Hold

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

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