Rational points on homogeneous varieties and Equidistribution of Adelic periods

Details Rational points on homogeneous varieties and Equidistribution of Adelic periods Rational points on homogeneous varieties and Equidistribution of Adelic periods

2008-03-13

arxiv.org/abs/0803.1996v3

Mathematics

Algebraic Geometry

Final version (59 pages +18 pages of Appendix), to appear in GAFA

Scientific paper

Let U:=L\G be a homogeneous variety defined over a number field K, where G is a connected semisimple K-group and L is a connected maximal semisimple K-subgroup of G with finite index in its normalizer. Assuming that G(K_v) acts transitively on U(K_v) for almost all places v of K, we obtain the asymptotic of the number of rational points in U(K) with height bounded by T, and settle new cases of Manin's conjecture for many wonderful varieties. The main ingredient of our approach is the equidistribution of semisimple adelic periods, which is established using the theory of unipotent flows.

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