Rational points on homogeneous varieties and equidistribution of adelic periods

Alex Gorodnik, Hee Oh, Mikhail Borovoi

Research output: Contribution to journalArticlepeer-review

Abstract

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(Kv) acts transitively on U(Kv) for almost all places v of K, we obtain an asymptotic for the number of rational points U(K) with height bounded by T as 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.

Original languageEnglish
Pages (from-to)319-392
Number of pages74
JournalGeometric and Functional Analysis
Volume21
Issue number2
DOIs
StatePublished - Apr 2011

Keywords

  • Manin conjecture
  • homogeneous dynamics
  • rational points
  • unipotent flows

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