Manin obstruction to strong approximation for homogeneous spaces

Mikhail Borovoi, Cyril Demarche

Research output: Contribution to journalArticlepeer-review

Abstract

Fora homogeneous spaceX (not necessarily principal)ofaconnected algebraic group G (not necessarily linear) over a number field k, we prove a theorem of strong approximation for the adelic points of X in the Brauer-Manin set. Namely, for an adelic point x of X orthogonal to a certain subgroup (which may contain transcendental elements) of the Brauer group Br.X/of X with respect to the Manin pairing, we prove a strong approximation property for x away from a finite set S of places of k. Our result extends a result of Harari for torsors of semiabelian varieties and a result of Colliot-Thélène and Xu for homogeneous spaces of simply connected semisimple groups, and our proof uses those results.

Original languageEnglish
Pages (from-to)1-54
Number of pages54
JournalCommentarii Mathematici Helvetici
Volume88
Issue number1
DOIs
StatePublished - 2013

Keywords

  • Brauer group
  • Connected algebraic groups
  • Homogeneous spaces
  • Manin obstruction
  • Strong approximation

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