The characteristic polynomials of abelian varieties of dimensions 4 over finite fields
نویسندگان
چکیده
We describe the set of characteristic polynomials of abelian varieties of dimension 4 over finite fields.
منابع مشابه
The characteristic polynomials of abelian varieties of dimensions 3 over finite fields
We describe the set of characteristic polynomials of abelian varieties of dimension 3 over finite fields.
متن کاملABELIAN VARIETIES OVER FINITE FIELDS WITH A SPECIFIED CHARACTERISTIC POLYNOMIAL MODULO l
We estimate the fraction of isogeny classes of abelian varieties over a finite field which have a given characteristic polynomial P (T ) modulo l. As an application we find the proportion of isogeny classes of abelian varieties with a rational point of order l.
متن کاملThe Tate Conjecture for Certain Abelian Varieties over Finite Fields
In an earlier work, we showed that if the Hodge conjecture holds for all complex abelian varieties of CM-type, then the Tate conjecture holds for all abelian varieties over finite fields (Milne 1999b). In this article, we extract from the proof a statement (Theorem 1.1) that sometimes allows one to deduce the Tate conjecture for the powers of a single abelian variety A over a finite field from ...
متن کاملUsing zeta functions to factor polynomials over finite fields
In 2005, Kayal suggested that Schoof’s algorithm for counting points on elliptic curves over finite fields might yield an approach to factor polynomials over finite fields in deterministic polynomial time. We present an exposition of his idea and then explain details of a generalization involving Pila’s algorithm for abelian varieties.
متن کاملSupersingular Abelian Varieties over Finite Fields
Let A be a supersingular abelian variety defined over a finite field k. We give an approximate description of the structure of the group A(k) of k-rational points of A in terms of the characteristic polynomial f of the Frobenius endomorphism of A relative to k. Write f = > gi i for distinct monic irreducible polynomials gi and positive integers ei . We show that there is a group homomorphism .:...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2017