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Modules over orders, conjugacy classes of integral matrices, and abelian varieties over finite fields
Stefano Marseglia
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We give an algorithm to compute representatives of the conjugacy classes of semisimple square integral matrices with given minimal and characteristic polynomials. We also give an algorithm to compute the 𝔽_q-isomorphism classes of abelian varieties over a finite field 𝔽_q which belong to an isogeny class determined by a characteristic polynomial h of Frobenius when h is ordinary, or q is prime and h has no real roots.
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