ABELIAN VARIETIES OVER NUMBER FIELDS, TAME RAMIFICATION AND BIG GALOIS IMAGE

作者：Arias De Reyna Sara^*; Kappen Christian

来源：Mathematical Research Letters, 2013, 20(1): 1-17.

DOI：10.4310/mrl.2013.v20.n1.a1

Given a natural number n %26gt;= 1 and a number field K, we show the existence of an integer l(0) such that for any prime number l %26gt;= 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 %26lt;br%26gt;rho(A,l) : G(F) -%26gt; GSp(A[l]((F) over bar)) %26lt;br%26gt;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%26apos;/F such that F is unramified above l.

• 出版日期2013