ON FINITE GALOIS STABLE ARITHMETIC GROUPS AND THEIR APPLICATIONS

Date

2008-12-01

Author

Khrebtova, Ekaterina S.
Malinin, Dmitry

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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

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Citation Formats

E. S. Khrebtova and D. Malinin, “ON FINITE GALOIS STABLE ARITHMETIC GROUPS AND THEIR APPLICATIONS,” JOURNAL OF ALGEBRA AND ITS APPLICATIONS, pp. 773–783, 2008, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/64704.