ON FINITE GALOIS STABLE ARITHMETIC GROUPS AND THEIR APPLICATIONS


Khrebtova E. S. , Malinin D.

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, cilt.7, ss.773-783, 2008 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 7 Konu: 6
  • Basım Tarihi: 2008
  • Doi Numarası: 10.1142/s0219498808003119
  • Dergi Adı: JOURNAL OF ALGEBRA AND ITS APPLICATIONS
  • Sayfa Sayıları: ss.773-783

Özet

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.