000			04706cam a2200649 i 4500
001			on1112422042
003			OCoLC
005			20220908100202.0
006			m o d
007			cr |||||||||||
008			190607t20192019nju ob 100 0 eng
010			_a 2021692895
040			_aDLC _beng _erda _epn _cDLC _dJSTOR _dOCLCF _dN$T _dYDX _dCNO _dOH1 _dIEEEE _dEBLCP _dOCLCO _dOCLCQ
020			_a9780691197548 _q(ebook)
020			_a0691197547
020			_z9780691193786 _q(hardback)
020			_z0691193789 _q(hardback)
020			_z9780691193779 _q(paperback)
020			_z0691193770 _q(paperback)
029	1		_aAU@ _b000066179724
035			_a(OCoLC)1112422042
037			_a22573/ctvft8mx7 _bJSTOR
037			_a9452323 _bIEEE
050	0	0	_aQA242.5
082	0	4	_a516.35 _223
049			_aMAIN
245	0	0	_aArithmetic and geometry : _bten years in Alpbach / _cedited by Gisbert W�ustholz and Clemens Fuchs.
264		1	_aPrinceton, New Jersey : _bPrinceton University Press, _c2019.
264		4	_c�2019
300			_a1 online resource (viii, 174 pages)
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aAnnals of mathematics studies ; _vnumber 202
504			_aIncludes bibliographical references.
505	0	0	_tPreface / _rGisbert W�ustholz -- _g1. _tIntroduction -- _g2. _tLocal Shimura varieties : minicourse given by Peter Scholze / _rSergey Gorchinskiy and Lars K�uhne -- _g3. _tHyperelliptic continued fractions and generalized Jacobians : minicourse given by Umberto Zannier / _rLaura Capuano, Peter Jossen, Christina Karolus, and Francesco Veneziano -- _g4. _tFaltings heights and L-functions : minicourse given by Shou-Wu Zhang / _rZiyang Gao, Rafael von K�anel, and Lucia Mocz.
520			_aArithmetic and Geometry presents highlights of recent work in arithmetic algebraic geometry by some of the world's leading mathematicians. Together, these 2016 lectures--which were delivered in celebration of the tenth anniversary of the annual summer workshops in Alpbach, Austria--provide an introduction to high-level research on three topics: Shimura varieties, hyperelliptic continued fractions and generalized Jacobians, and Faltings height and L-functions. The book consists of notes, written by young researchers, on three sets of lectures or minicourses given at Alpbach. The first course, taught by Peter Scholze, contains his recent results dealing with the local Langlands conjecture. The fundamental question is whether for a given datum there exists a so-called local Shimura variety. In some cases, they exist in the category of rigid analytic spaces; in others, one has to use Scholze's perfectoid spaces. The second course, taught by Umberto Zannier, addresses the famous Pell equation--not in the classical setting but rather with the so-called polynomial Pell equation, where the integers are replaced by polynomials in one variable with complex coefficients, which leads to the study of hyperelliptic continued fractions and generalized Jacobians. The third course, taught by Shou-Wu Zhang, originates in the Chowla-Selberg formula, which was taken up by Gross and Zagier to relate values of the L-function for elliptic curves with the height of Heegner points on the curves. Zhang, X. Yuan, and Wei Zhang prove the Gross-Zagier formula on Shimura curves and verify the Colmez conjecture on average.-- _cSource other than the Library of Congress.
588	0		_aPrint version record and CIP data provided by publisher; resource not viewed.
590			_aIEEE _bIEEE Xplore Princeton University Press eBooks Library
650		0	_aArithmetical algebraic geometry _vCongresses. _965394
650		6	_aG�eom�etrie alg�ebrique arithm�etique _vCongr�es. _965395
650		7	_aArithmetical algebraic geometry. _2fast _0(OCoLC)fst00814526 _965396
655		2	_aCongress _965397
655		7	_aConference papers and proceedings. _2fast _0(OCoLC)fst01423772 _94691
655		7	_aConference papers and proceedings. _2lcgft _94691
655		7	_aActes de congr�es. _2rvmgf _965398
700	1		_aW�ustholz, Gisbert, _eeditor. _965399
700	1		_aFuchs, Clemens, _d1976- _eeditor. _965400
776	0	8	_iPrint version: _tArithmetic and geometry. _dPrinceton, New Jersey : Princeton University Press, 2019 _z9780691193786 _w(DLC) 2019943220
830		0	_aAnnals of mathematics studies ; _vno. 202. _965401
856	4	0	_uhttps://ieeexplore.ieee.org/servlet/opac?bknumber=9452323
938			_aProQuest Ebook Central _bEBLB _nEBL5850001
938			_aEBSCOhost _bEBSC _n2101957
938			_aYBP Library Services _bYANK _n16356142
942			_cEBK
994			_a92 _bINTKS
999			_c81453 _d81453