Arithmetic of Higher-Dimensional Algebraic Varieties [electronic resource] /

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.

Bibliographic Details

Main Authors:	Poonen, Bjorn. editor., Tschinkel, Yuri. editor., SpringerLink (Online service)
Format:	Texto biblioteca
Language:	eng
Published:	Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser, 2004
Subjects:	Mathematics., Algebraic geometry., Algebra., Field theory (Physics)., Functions of complex variables., Number theory., Number Theory., Algebraic Geometry., Field Theory and Polynomials., Several Complex Variables and Analytic Spaces.,
Online Access:	http://dx.doi.org/10.1007/978-0-8176-8170-8
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