scholarly journals Abelian varieties over finite fields with a specified characteristic polynomial modulo \ell

2004 ◽  
Vol 16 (1) ◽  
pp. 173-178 ◽  
Author(s):  
Joshua Holden
Keyword(s):  
Characteristic Polynomial ◽  
Finite Fields ◽  
Abelian Varieties

scholarly journals Computing abelian varieties over finite fields isogenous to a power

2019 ◽  
Vol 5 (4) ◽  
Author(s):  
Stefano Marseglia
Keyword(s):  
Characteristic Polynomial ◽  
Finite Fields ◽  
Abelian Varieties ◽  
Number Fields ◽  
Explicit Description ◽  
Finite Product ◽  
Real Roots ◽  
Isomorphism Classes ◽  
Ordinary Case ◽  
Theoretic Description

Abstract In this paper we give a module-theoretic description of the isomorphism classes of abelian varieties A isogenous to $$B^r$$Br, where the characteristic polynomial g of Frobenius of B is an ordinary square-free q-Weil polynomial, for a power q of a prime p, or a square-free p-Weil polynomial with no real roots. Under some extra assumptions on the polynomial g we give an explicit description of all the isomorphism classes which can be computed in terms of fractional ideals of an order in a finite product of number fields. In the ordinary case, we also give a module-theoretic description of the polarizations of A.

scholarly journals Quadratic form Approach for the Number of Zeros of Homogeneous Linear Recurring Sequences over Finite Fields

2017 ◽  
Vol 9 (3) ◽  
pp. 8
Author(s):  
Yasanthi Kottegoda
Keyword(s):  
Quadratic Form ◽  
Finite Field ◽  
Characteristic Polynomial ◽  
Finite Fields ◽  
Quadratic Forms ◽  
Linear Recurring Sequences ◽  
Exact Number ◽  
Number Of Zeros ◽  
Homogeneous Linear ◽  
Form Approach

We consider homogeneous linear recurring sequences over a finite field $\mathbb{F}_{q}$, based on an irreducible characteristic polynomial of degree $n$ and order $m$. Let $t=(q^{n}-1)/ m$. We use quadratic forms over finite fields to give the exact number of occurrences of zeros of the sequence within its least period when $t$ has q-adic weight 2. Consequently we prove that the cardinality of the set of zeros for sequences from this category is equal to two.

scholarly journals Counting Points on Curves and Abelian Varieties Over Finite Fields

2001 ◽  
Vol 32 (3) ◽  
pp. 171-189 ◽  
Author(s):  
Leonard M. Adleman ◽  
Ming-Deh Huang
Keyword(s):  
Finite Fields ◽  
Abelian Varieties ◽  
Counting Points
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