On the genera of semisimple groups defined over an integral domain of a global function field

Rony A. Bitan

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

Let K = F q (C) be the global function field of rational functions over a smooth and projective curve C defined over a finite field F q . The ring of regular functions on C − S Where S ≠ ∅ is any finite set of closed points on C is a Dedekind domain O S of K. For a semisimple O S -group G With a smooth fundamental group F, We aim to describe both the set of genera of G and its principal genus (the latter if G ⊗ OS K is isotropic at S) in terms of abelian groups depending on O S and F only. This leads to a necessary and sufficient condition for the Hasse local-global principle to hold for certain G. We also use it to express the TamagaWa number τ(G) of a semisimple K-group G by the Euler–Poincaré invariant. This facilitates the computation of τ(G) for tWisted K-groups.

Original languageEnglish
Pages (from-to)1037-1057
Number of pages21
JournalJournal de Theorie des Nombres de Bordeaux
Volume30
Issue number3
DOIs
StatePublished - 2018

Bibliographical note

Publisher Copyright:
© Société Arithmétique de Bordeaux, 2018,.

Keywords

  • Class number
  • Hasse principle
  • Mots-clefs
  • Tamagawa number

Fingerprint

Dive into the research topics of 'On the genera of semisimple groups defined over an integral domain of a global function field'. Together they form a unique fingerprint.

Cite this