000 01709cam a22002778i 4500
001 135871
003 ISI Library, Kolkata
005 20150616115016.0
008 140620s2014 riu b 001 0 eng
020 _a9781470418823 (alk. paper)
040 _aISI Library
082 0 0 _a510MS
_223
_bAm512
100 1 _aJahnel, Jorg.
245 1 0 _aBrauer groups, tamagawa measures, and rational points on algebraic varieties /
_cJorg Jahnel.
260 _aProvidence :
_bAmerican Mathematical Society,
_cc2014.
300 _aviii, 267 p. :
_billustrations ;
_c27 cm.
490 0 _aMathematical surveys and monographs ;
_vv 198
504 _aIncludes bibliographical references and index.
505 0 _aIntroduction-- Part A. Heights-- I. The concept of a height-- II. Conjectures on the asymptotics of points of bounded height-- Part B. The Brauer group-- III. On the Brauer group of a scheme-- IV. An application: The Brauer-Manin obstruction-- Part C. Numerical experiments V. The Diophantine equation x4+2y4=z4+4w4-- VI. Points of bounded height on cubic and quartic threefolds-- VII. On the smallest point on a diagonal cubic surface-- Appendix-- Bibliography-- Index.
520 _aThe central theme of this book is the study of rational points on algebraic varieties of Fano and intermediate type - both in terms of when such points exist and, if they do, their quantitative density. The book presents the state of the art in computational arithmetic geometry for higher-dimensional algebraic varieties.
650 0 _aAlgebraic varieties.
650 0 _aAlgebraic Geometry.
650 0 _aBrauer groups.
650 0 _aRational points (Geometry).
942 _2ddc
_cBK
999 _c419032
_d419032