On finite arithmetic groups

Dmitry Malinin

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

Let F be a finite extension of ℚ, ℚp or a global field of positive characteristic, and let E/F be a Galois extension. We study the realization fields of finite subgroups G of GLn(E) stable under the natural operation of the Galois group of E/F. Though for suffciently large n and a fixed algebraic number field F every its finite extension E is realizable via adjoining to F the entries of all matrices g ε G for some finite Galois stable subgroup G of GLn(ℂ), there is only a finite number of possible realization field extensions of F if G ⊂ GLn(OE) over the ring OE of integers of E. After an exposition of earlier results we give their refinements for the realization fields E/F. We consider some applications to quadratic lattices, arithmetic algebraic geometry and Galois cohomology of related arithmetic groups.

Original languageEnglish
Pages (from-to)199-227
Number of pages29
JournalInternational Journal of Group Theory
Volume2
Issue number1
Publication statusPublished - 2013

Keywords

  • Algebraic integers
  • Galois groups
  • Integral representations
  • Realization fields

ASJC Scopus subject areas

  • Algebra and Number Theory

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