منابع مشابه
Endomorphism fields of abelian varieties
We give a sharp divisibility bound, in terms of g, for the degree of the field extension required to realize the endomorphisms of an abelian variety of dimension g over an arbitrary number field; this refines a result of Silverberg. This follows from a stronger result giving the same bound for the order of the component group of the Sato–Tate group of the abelian variety, which had been proved ...
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Generalizing a method of Sutherland and the author for elliptic curves [5, 1], we design a subexponential algorithm for computing the endomorphism ring structure of ordinary abelian varieties of dimension two over finite fields. Although its correctness and complexity bound rely on several assumptions, we report on practical computations showing that it performs very well and can easily handle ...
متن کاملModuli of Supersingular Abelian Varieties with Endomorphism Structure
0 Introduction In this paper, we investigate the moduli space S g,L of supersingular abelian varieties X with endomorphism structure θ : O L → End(X) and O L-linear principal polarization, where O L is the ring of integers in an algebraic number field L with involution *. General existence of the coarse moduli scheme of polarized abelian varieties with endomorphism structure is shown by using t...
متن کاملEndomorphism rings of Abelian varieties and their representations
These are notes of two talks with the aim of giving some basic properties of the endomorphism ring of an Abelian variety A and its representations on certain linear objects associated to A. The results can be found in § 5.1 of Shimura’s book [1], but presented in a completely different way. For completeness, we state some definitions. An Abelian variety over a field k is a proper, smooth, conne...
متن کاملAbelian 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...
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ژورنال
عنوان ژورنال: Research in Number Theory
سال: 2017
ISSN: 2363-9555
DOI: 10.1007/s40993-017-0088-4