On finite galois stable arithmetic groups and their applications

Ekaterina S. Khrebtova, Dmitry Malinin

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

We prove the existence and finiteness theorems for integral representations stable under Galois operation. An explicit construction of the realization fields for representations of finite groups stable under the natural operation of the Galois group is given. We also compare the representations over fields and the rings of integers, and give a quantitative result on the rarity of integral Galois stable representations. There is a series of related conjectures and applications to arithmetic algebraic geometry, finite flat group schemes, positive definite quadratic lattices and Galois cohomology.

Original languageEnglish
Pages (from-to)773-783
Number of pages11
JournalJournal of Algebra and its Applications
Volume7
Issue number6
DOIs
Publication statusPublished - 2008
Externally publishedYes

Keywords

  • Algebraic integers
  • Galois algebras
  • Galois group
  • Integral representations

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Applied Mathematics

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