MARC Record from marc_columbia

LEADER: 04545cam a2200589 i 4500
001 14447596
005 20200207141818.0
008 190411t20192019riua b 100 0 eng
010 $a 2019016582
035 $a(OCoLC)on1099546301
040 $aDLC$beng$erda$cDLC$dOCLCO$dOCLCF$dYDX$dBUF$dYDX$dKSU$dMTG$dSTF$dUKMGB
015 $aGBB9J3968$2bnb
016 7 $a019627319$2Uk
020 $a9781470450151$qhardcover$qalkaline paper
020 $a1470450151$qhardcover$qalkaline paper
035 $a(OCoLC)1099546301
042 $apcc
050 00 $aQA247$b.A75 2017
050 4 $aQA247$b.A759 2017
082 00 $a516.3/5$bA7199p$223
084 $a11F80$a11G25$a14C30$a14F30$a14F40$a14G20$a14G22$a14G35$a14G40$a14L05$2msc
049 $aZCUA
111 2 $aArizona Winter School on Perfectoid Spaces$n(20th :$d2017 :$cTucson, Ariz.),$jauthor.
245 10 $aPerfectoid spaces :$blectures from the 2017 Arizona Winter School /$cBhargav Bhatt [and 3 others] ; with an introduction by Peter Scholze ; Bryden Cais, editor.
264 1 $aProvidence, Rhode Island :$bAmerican Mathematical Society,$c[2019]
264 4 $c©2019
300 $axii, 297 pages :$billustrations ;$c27 cm.
336 $atext$btxt$2rdacontent
337 $aunmediated$bn$2rdamedia
338 $avolume$bnc$2rdacarrier
490 1 $aMathematical surveys and monographs ;$vvolume 242
500 $aPrepared for the twentieth Arizona Winter School on Perfectoid Spaces, held March 11-17, 2017, at the University of Arizona in Tucson.
504 $aIncludes bibliographical references.
520 $aIntroduced by Peter Scholze in 2011, perfectoid spaces are a bridge between geometry in characteristic 0 and characteristic p, and have been used to solve many important problems, including cases of the weight-monodromy conjecture and the association of Galois representations to torsion classes in cohomology. This book, originating from a series of lectures given at the 2017 Arizona Winter School on perfectoid spaces, provides a broad introduction to the subject. After an introduction with insight into the history and future of the subject by Peter Scholze, Jared Weinstein gives a user-friendly and utilitarian account of the theory of adic spaces. Kiran Kedlaya further develops the foundational material, studies vector bundles on Fargues-Fontaine curves, and introduces diamonds and shtukas over them with a view toward the local Langlands correspondence. Bhargav Bhatt explains the application of perfectoid spaces to comparison isomorphisms in p-adic Hodge theory. Finally, Ana Caraiani explains the application of perfectoid spaces to the construction of Galois representations associated to torsion classes in the cohomology of locally symmetric spaces for the general linear group. -- Publisher's description.
505 00 $tPreface /$rby Bryden Cais --$tIntroduction /$rby Peter Scholze --$tAdic spaces /$rby Jared Weinstein --$tSheaves, stacks, and shtukas /$rby Kiran S. Kedlaya --$tThe Hodge-Tate decomposition via perfectoid spaces /$rby Bhargav Bhatt --$tPerfectoid Shimura varieties /$rby Ana Caraiani.
650 0 $aTopological fields.
650 7 $aTopological fields.$2fast$0(OCoLC)fst01152682
650 7 $aNumber theory -- Discontinuous groups and automorphic forms -- Galois representations.$2msc
650 7 $aNumber theory -- Arithmetic algebraic geometry (Diophantine geometry) -- Varieties over finite and local fields.$2msc
650 7 $aAlgebraic geometry -- Cycles and subschemes -- Transcendental methods, Hodge theory.$2msc
650 7 $aAlgebraic geometry -- (Co)homology theory -- $p$-adic cohomology, crystalline cohomology.$2msc
650 7 $aAlgebraic geometry -- (Co)homology theory -- de Rham cohomology.$2msc
650 7 $aAlgebraic geometry -- Arithmetic problems. Diophantine geometry -- Local ground fields.$2msc
650 7 $aAlgebraic geometry -- Arithmetic problems. Diophantine geometry -- Rigid analytic geometry.$2msc
650 7 $aAlgebraic geometry -- Arithmetic problems. Diophantine geometry -- Modular and Shimura varieties.$2msc
650 7 $aAlgebraic geometry -- Arithmetic problems. Diophantine geometry -- Arithmetic varieties and schemes; Arakelov theory; heights.$2msc
650 7 $aAlgebraic geometry -- Algebraic groups -- Formal groups, $p$-divisible groups.$2msc
700 1 $aBhatt, Bhargav,$d1983-$eauthor.
700 1 $aScholze, Peter.
700 1 $aCais, Bryden,$eeditor.
830 0 $aMathematical surveys and monographs ;$vno. 242.
852 00 $bmat$hQA247$i.A75 2017