32 citations · 94 across the 30 of their papers we have counts for
8 papers · 1 filter
Computing algorithm for reduction type of CM abelian varieties
Artyom Smirnov, Alexey Zaytsev
Let be an abelian variety over a number field, with a good reduction at a prime ideal containing a prime number . Denote by an abelian variety over a fin…
Generalization of Deuring Reduction Theorem
Alexey Zaytsev
In this paper we generalize the Deuring theorem on a reduction of elliptic curve with complex multiplication. More precisely, for an Abelian variety , arising after reduction of…
Characteristic Polynomial of Supersingular Abelian Varieties over Finite Fields
Vijaykumar Singh, Gary McGuire, Alexey Zaytsev
In this article, we give a complete description of the characteristic polynomials of supersingular abelian varieties over finite fields. We list them for the dimensions upto 7.
The Number of Rational Points On Genus 4 Hyperelliptic Supersingular Curves in Characteristic 2
Gary McGuire, Alexey Zaytsev
One of the big questions in the area of curves over finite fields concerns the distribution of the numbers of points: Which numbers occur as the number of points on a curve of genu…
On the Zeta Functions of an optimal tower of function fields over $\FF_4$
Alexey Zaytsev, Gary McGuire
In this paper we derive a recursion for the zeta function of each function field in the second Garcia-Stichtenoth tower when . We obtain our recursion by applying a theorem of…
Optimal Curves of Genus 3 over Finite Fields with Discriminant -19
E. Alekseenko, S. Aleshnikov, N. Markin +1
In this work we study the properties of maximal and minimal curves of genus 3 over finite fields with discriminant -19. We prove that any such curve can be given by an explicit equ…