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Arithmetic of Higher-Dimensional Algebraic Varieties / edited by Bjorn Poonen, Yuri Tschinkel
(Progress in Mathematics. ISSN:2296505X ; 226)
版 | 1st ed. 2004. |
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出版者 | (Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser) |
出版年 | 2004 |
大きさ | XVI, 287 p : online resource |
著者標目 | Poonen, Bjorn editor Tschinkel, Yuri editor SpringerLink (Online service) |
件 名 | LCSH:Number theory LCSH:Algebraic geometry LCSH:Algebraic fields LCSH:Polynomials LCSH:Functions of complex variables FREE:Number Theory FREE:Algebraic Geometry FREE:Field Theory and Polynomials FREE:Several Complex Variables and Analytic Spaces |
一般注記 | Diophantine equations: progress and problems -- Rational points and analytic number theory -- Weak approximation on algebraic varieties -- Counting points on varieties using universal torsors -- The Cox ring of a Del Pezzo surface -- Counting rational points on threefolds -- Remarques sur l’approximation faible sur un corps de fonctions d’une variable -- K3 surfaces over number fields with geometric Picard number one -- Jumps in Mordell-Weil rank and Arithmetic Surjectivity -- Universal torsors and Cox rings -- Random diophantine equations -- Descent on simply connected surfaces over algebraic number fields -- Rational points on compactifications of semi-simple groups of rank 1 -- Weak Approximation on Del Pezzo surfaces of degree 4 -- Transcendental Brauer-Manin obstruction on a pencil of elliptic curves One of the great successes of twentieth century mathematics has been the remarkable qualitative understanding of rational and integral points on curves, gleaned in part through the theorems of Mordell, Weil, Siegel, and Faltings. It has become clear that the study of rational and integral points has deep connections to other branches of mathematics: complex algebraic geometry, Galois and étale cohomology, transcendence theory and diophantine approximation, harmonic analysis, automorphic forms, and analytic number theory. This text, which focuses on higher-dimensional varieties, provides precisely such an interdisciplinary view of the subject. It is a digest of research and survey papers by leading specialists; the book documents current knowledge in higher-dimensional arithmetic and gives indications for future research. It will be valuable not only to practitioners in the field, but to a wide audience of mathematicians and graduate students with an interest in arithmetic geometry. Contributors: Batyrev, V.V.; Broberg, N.; Colliot-Thélène, J-L.; Ellenberg, J.S.; Gille, P.; Graber, T.; Harari, D.; Harris, J.; Hassett, B.; Heath-Brown, R.; Mazur, B.; Peyre, E.; Poonen, B.; Popov, O.N.; Raskind, W.; Salberger, P.; Scharaschkin, V.; Shalika, J.; Starr, J.; Swinnerton-Dyer, P.; Takloo-Bighash, R.; Tschinkel, Y.: Voloch, J.F.; Wittenberg, O HTTP:URL=https://doi.org/10.1007/978-0-8176-8170-8 |
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電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
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電子ブック | オンライン | 電子ブック |
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Springer eBooks | 9780817681708 |
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電子リソース |
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EB00197117 |
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データ種別 | 電子ブック |
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分 類 | LCC:QA241-247.5 DC23:512.7 |
書誌ID | 4000104659 |
ISBN | 9780817681708 |
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