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Abelian Varieties Over Finite Fields
The Integral Classical Groups and Their Automorphisms
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abelian extension Abelian variety algebraic extension algebraic number field algebraically closed algebraically independent apply arithmetic assume automorphisms bound class field theory class formation class group class number coefficients cohomology complete compute condition conjecture constant contains COROLLARY corresponding cyclotomic definition degree denote depends dimension diophantine equation divisor domain elements elliptic curves estimate example exists extension finite field fixed follows formula function field Galois group genus geometric given gives Hence Henselian homomorphism ideal implies inequality infinite irreducible isogeny isomorphism Lemma linear linearly independent Math matrix maximal method multiplicative nonsingular number theory obtain ord F plane polynomial problem profinite group proof of Theorem Proposition proved quadratic field quadratic forms rational relation representation residue roots of unity satisfies sequence sieve solutions space subgroup Suppose transcendental trivial unique unramified valuation subring values variables vector zero zeta function