Reference : Abelian varieties over number fields, tame ramification and big Galois image
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/12896
Abelian varieties over number fields, tame ramification and big Galois image
English
Arias De Reyna Dominguez, Sara mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Kappen, Christian [Institut für Experimentelle Mathematik, University of Duisburg-Essen]
2013
Mathematical Research Letters
International Press of Boston, Inc.
20
01
1-17
Yes (verified by ORBilu)
International
1073-2780
[en] Given a natural number n ≥ 1 and a number field K, we show the existence of an integer l_0 such that for any prime number l ≥ l_0 , there exists a finite extension F/K, unramified in all places above l, together with a principally polarized abelian variety A of dimension n over F such that the resulting l-torsion representation ρ_{A,l} : G_F → GSp(A[l]) is surjective and everywhere tamely ramified. In particular, we realize GSp_{2n}(F_l) as the Galois group of a finite tame extension of number fields F' /F such that F is unramified above l.
Researchers
http://hdl.handle.net/10993/12896

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