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ON FINITE GALOIS STABLE ARITHMETIC GROUPS AND THEIR APPLICATIONS
Date
2008-12-01
Author
Khrebtova, Ekaterina S.
Malinin, Dmitry
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This work is licensed under a
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
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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.
Subject Keywords
Algebra and Number Theory
,
Applied Mathematics
URI
https://hdl.handle.net/11511/64704
Journal
JOURNAL OF ALGEBRA AND ITS APPLICATIONS
DOI
https://doi.org/10.1142/s0219498808003119
Collections
Department of Mathematics, Article