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Title

On finite arithmetic groups

Year: 1392
COI: JR_THEGR-2-1_017
Language: EnglishView: 23
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Authors

Dmitry Malinin - I.H.E.S.

Abstract:

Let F be a finite extension of \Bbb Q‎, ‎{\Bbb Q}_p 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 GL_n(E) stable under the natural‎ ‎operation of the Galois group of E/F‎. ‎Though for sufficiently 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\in G for some finite Galois stable subgroup G of GL_n(\Bbb C)‎, ‎there is only a‎ ‎finite number of possible realization field extensions of F if G\subset GL_n(O_E) over the‎ ‎ring O_E 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.

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This Paper COI Code is JR_THEGR-2-1_017. Also You can use the following address to link to this article. This link is permanent and is used as an article registration confirmation in the Civilica reference:

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Malinin, Dmitry,1392,On finite arithmetic groups,https://civilica.com/doc/1199967

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