Journal of the Ramanujan Mathematical Society

J. L. Colliot-Thelene ¹, J. N. Iyer ²

Affiliations
1 CNRS, UMR 8628, Mathematiques, Batiment 425, Universite Paris-Sud, F-91405 Orsay, FR
2 The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600 113, IN

Abstract

For a smooth, projective family of homogeneous varieties defined over a number field, we show that if potential density holds for the rational points of the base, then it also holds for the total space. A conjecture of Campana and Peternell, known in dimension at most 4 and for certain higher dimensional cases, would then imply potential density for the rational points of smooth projective varieties over number fields whose tangent bundle is nef.

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J. L. Colliot-Thelene ¹, B. E. Kunyavskii ²

Affiliations
1 C.N.R.S. URA D0752, Mathematiques, Batiment 425 Universite de Paris-Sud, F-91405 Orsay, FR
2 Department of Mathematics and Computer Science Bar-Ilan University, 52900 Ramat-Gan, IL

Abstract

Let G be a connected linear algebraic group over a field k of characteristic zero. Let E be a principal homogeneous space under G and let X be a smooth K-compactification of E. Under a hypothesis which covers both the case where G is semi-simple and the case where G is a torus, we give an "algebraic" formula for the Brauer group of X. The proof proceeds by reduction to the case of finite fields.

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