MARC Record from marc_columbia

LEADER: 02824cam a2200385Ii 4500
001 11547121
005 20150920222234.0
008 150707t20152015fr a b 000 0 eng d
020 $a9782856298077$q(pbk.)
020 $a2856298079$q(pbk.)
029 1 $aNLGGC$b394348591
035 $a(OCoLC)ocn913077122
035 $a(OCoLC)913077122
035 $a(NNC)11547121
040 $aLWU$beng$erda$cLWU$dOCLCO$dUIU$dIQU$dFDA$dYDXCP$dBTCTA$dWAU$dCOD
041 0 $aeng$beng$bfre
050 4 $aQA564$b.K43 2015
100 1 $aKedlaya, Kiran Sridhara,$d1974-$eauthor.
245 10 $aRelative p-adic Hodge theory :$bfoundations /$cKiran S. Kedlaya, Ruochuan Liu.
264 1 $aParis :$bSociété mathématique de France,$c2015.
264 4 $c©2015
300 $a239 pages :$billustrations ;$c24 cm.
336 $atext$btxt$2rdacontent
337 $aunmediated$bn$2rdamedia
338 $avolume$bnc$2rdacarrier
490 1 $aAstérisque,$x0303-1179 ;$v371
504 $aIncludes 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 $aAbstract also in French.
650 0 $aHodge theory.
650 0 $ap-adic fields.
650 0 $aGeometry, Algebraic.
700 1 $aLiu, Ruochuan,$eauthor.
830 0 $aAstérisque ;$v371.
852 00 $bmat$hQA1$i.A82 v.371