On Classification of Groups of Points on Abelian Varieties over Finite Fields
نویسندگان
چکیده
منابع مشابه
Groups of Points on Abelian Varieties over Finite Fields
Fix an isogeny class of abelian varieties with commutative endomorphism algebra over a finite field. This isogeny class is determined by a Weil polynomial fA without multiple roots. We give a classification of groups of k-rational points on varieties from this class in terms of Newton polygons of fA(1− t).
متن کاملGroups of Rational Points on Abelian Varieties over Finite Fields
Fix an isogeny class of abelian varieties with commutative endomorphism algebra over a finite field. This isogeny class is determined by a Weil polynomial fA without multiple roots. We give a classification of groups of rational points on varieties from this class in terms of Newton polygons of fA(1− t).
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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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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...
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ژورنال
عنوان ژورنال: Moscow Mathematical Journal
سال: 2015
ISSN: 1609-3321,1609-4514
DOI: 10.17323/1609-4514-2015-15-4-805-815