• Discrete subgroups of algebraic groups over local fields of positive characteristics

    • Fulltext

       

        Click here to view fulltext PDF


      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/099/02/0127-0146

    • Keywords

       

      Discrete subgroups; algebraic groups; local fields; Siegel domains; fundamental domains; positive characteristics

    • Abstract

       

      It is shown in this paper that ifG is the group ofk-points of a semisimple algebraic groupG over a local fieldk of positive characteristic such that all itsk-simple factors are ofk-rank 1 and Γ ⊂G is a non-cocompact irreducible lattice then Γ admits a fundamental domain which is a union of translates of Siegel domains. As a consequence we deduce that ifG has more than one simple factor, then Γ is finitely generated and by a theorem due to Venkataramana, it is arithmetic.

    • Author Affiliations

       

      M S Raghunathan1

      1. School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay - 400005, India
    • Dates

       
  • Proceedings – Mathematical Sciences | News

    • Editorial Note on Continuous Article Publication

      Posted on July 25, 2019

      Click here for Editorial Note on CAP Mode

© 2017-2019 Indian Academy of Sciences, Bengaluru.