Read e-book online Arithmetic of higher-dimensional algebraic varieties PDF

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By Bjorn Poonen, Yuri Tschinkel

ISBN-10: 081763259X

ISBN-13: 9780817632595

One of many nice successes of 20th century arithmetic has been the impressive qualitative knowing of rational and fundamental issues on curves, gleaned partly in the course of the theorems of Mordell, Weil, Siegel, and Faltings. It has develop into transparent that the learn of rational and critical issues has deep connections to different branches of arithmetic: advanced algebraic geometry, Galois and ,tale cohomology, transcendence concept and diophantine approximation, harmonic research, automorphic types, and analytic quantity thought. this article, which makes a speciality of larger dimensional types, offers accurately such an interdisciplinary view of the topic. it's a digest of analysis and survey papers by way of major experts; the e-book records present wisdom in higher-dimesional mathematics and provides symptoms for destiny study. will probably be precious not to in basic terms to practitioners within the box, yet to a large viewers of mathematicians and graduate scholars with an curiosity in mathematics geometry. members contain: P. Swinnerton-Dyer * B. Hassett * Yu. Tschinkel * J. Shalika * R. Takloo-Bighash * J.-L. Colliot-Th,lSne * A. de Jong * Ph. Gille * D. Harari * J. Harris * B. Mazur * W. Raskind * J. Starr * T. Wooley

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3) 80(2000), 513-544. [43] Sir Peter Swinnerton-Dyer, Weak approximation and R-equivalence on Cubic Surfaces, in Rational points on algebraic varieties (ed. Tschinkel) pp. 357-404 (Birkh¨auser, 2001). [44] Sir Peter Swinnerton-Dyer, The solubility of diagonal cubic surfaces, ´ Norm. Sup. (4) 34(2001), 891-912. Ann. Scient. Ec. Tate, On the conjectures of Birch and Swinnerton-Dyer and a geometric analog, S´em. Bourbaki 306(1966). , Cambridge, 1997).

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39(2002), 455-474. Skorobogatov, Weak approximation for surfaces defined by two quadratic forms, Duke J. Math. 63(1991), 517-536. Serre, Facteurs locaux des fonctions zˆeta des vari´et´es alg´ebriques (d´efinitions et conjectures), S´eminaire Delange-Pisot-Poitou 1969/70, exp. 19. Siegel, Normen algebraischer Zahlen, (Werke, Band IV, 250-268). Silverberg, Open Questions in Arithmetic Algebraic Geometry, in Arithmetic Algebraic Geometry pp. Skorobogatov, Beyond the Manin obstruction, Inv. Math. 135(1999), 399-424.

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Arithmetic of higher-dimensional algebraic varieties by Bjorn Poonen, Yuri Tschinkel

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