Finite group subschemes of abelian varieties over finite fields
نویسندگان
چکیده
منابع مشابه
Abelian varieties over finite fields
A. Weil proved that the geometric Frobenius π = Fa of an abelian variety over a finite field with q = pa elements has absolute value √ q for every embedding. T. Honda and J. Tate showed that A 7→ πA gives a bijection between the set of isogeny classes of simple abelian varieties over Fq and the set of conjugacy classes of q-Weil numbers. Higher-dimensional varieties over finite fields, Summer s...
متن کاملGroup Structures of Elementary Supersingular Abelian Varieties over Finite Fields
Let A be a supersingular abelian variety over a finite field k which is k-isogenous to a power of a simple abelian variety over k. Write the characteristic polynomial of the Frobenius endomorphism of A relative to k as f = g for a monic irreducible polynomial g and a positive integer e. We show that the group of k-rational points A(k) on A is isomorphic to (Z g(1) Z) unless A's simple component...
متن کاملEndomorphisms of Abelian Varieties over Finite Fields
Almost all of the general facts about abelian varieties which we use without comment or refer to as "well known" are due to WEIL, and the references for them are [12] and [3]. Let k be a field, k its algebraic closure, and A an abelian variety defined over k, of dimension g. For each integer m > 1, let A m denote the group of elements aeA(k) such that ma=O. Let l be a prime number different fro...
متن کاملHomomorphisms of Abelian Varieties over Finite Fields
The aim of this note is to give a proof of Tate’s theorems on homomorphisms of abelian varieties over finite fields [22, 8], using ideas of [26, 27]. We give a unified treatment for both l 6= p and l = p cases. In fact, we prove a slightly stronger version of those theorems with “finite coefficients”. I am grateful to Frans Oort and Bill Waterhouse for useful discussions. My special thanks go t...
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
ژورنال
عنوان ژورنال: Finite Fields and Their Applications
سال: 2014
ISSN: 1071-5797
DOI: 10.1016/j.ffa.2014.04.001