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Malinin, Dmitry. (1391). On finite arithmetic groups. , 2(1), 199-227. doi: 10.22108/ijgt.2013.2865
Dmitry Malinin. "On finite arithmetic groups". , 2, 1, 1391, 199-227. doi: 10.22108/ijgt.2013.2865
Malinin, Dmitry. (1391). 'On finite arithmetic groups', , 2(1), pp. 199-227. doi: 10.22108/ijgt.2013.2865
Malinin, Dmitry. On finite arithmetic groups. , 1391; 2(1): 199-227. doi: 10.22108/ijgt.2013.2865

On finite arithmetic groups

International Journal of Group Theory
مقاله 17، دوره 2، شماره 1، خرداد 2013، صفحه 199-227    اصل مقاله (600.01 K)
نوع مقاله: Ischia Group Theory 2012
شناسه دیجیتال (DOI): 10.22108/ijgt.2013.2865
نویسنده
Dmitry Malinin*
I.H.E.S.
چکیده
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.
کلیدواژه‌ها
algebraic integers؛ Galois groups؛ integral representations؛ realization fields
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