Arithmetic invariant theory II: Pure inner forms and obstructions to the existence of orbits

Manjul Bhargava, Benedict H. Gross, Xiaoheng Wang

Research output: Contribution to journalArticle

4 Scopus citations

Abstract

Let k be a field, let G be a reductive group, and let V be a linear representation of G. Let V//G = Spec(Sym*(V*))G denote the geometric quotient and let π:V→V//G denotethequotientmap.Arithmeticinvarianttheorystudiesthe map on the level of k-rational points. In this article, which is a continuation of the results of our earlier paper “Arithmetic invariant theory”, we provide necessary and sufficient conditions for a rational element of V// G to lie in the image of, π assuming that generic stabilizers are abelian. We illustrate the various scenarios that can occur with some recent examples of arithmetic interest.

Original languageEnglish (US)
Pages (from-to)139-171
Number of pages33
JournalProgress in Mathematics
Volume312
DOIs
StatePublished - Jan 1 2015

All Science Journal Classification (ASJC) codes

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

Keywords

  • Galois cohomology
  • Representation theory

Fingerprint Dive into the research topics of 'Arithmetic invariant theory II: Pure inner forms and obstructions to the existence of orbits'. Together they form a unique fingerprint.

  • Cite this