On Supersingular Abelian Varieties of Dimension Two over Finite Fields
β Scribed by Chaoping Xing
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 243 KB
- Volume
- 2
- Category
- Article
- ISSN
- 1071-5797
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β¦ Synopsis
In this paper we study the characteristic polynomials and the rational point group structure of supersingular varieties of dimension two over finite fields. Meanwhile, we also list all L-functions of supersingular curves of genus two over β«ήβ¬ 2 and determine the group structure of their divisor class groups over all finite algebraic extension of β«ήβ¬ 2 .
π SIMILAR VOLUMES
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 e for a monic irreducible polynomial g and a positive integer e. We show th
We develop efficient methods for deterministic computations with semi-algebraic sets and apply them to the problem of counting points on curves and Abelian varieties over finite fields. For Abelian varieties of dimension g in projective N space over Fq, we improve Pila's result and show that the pro
This paper was written at the University of Massachusetts at Amherst. We thank the working seminar on Shimura varieties there for patiently listening to us as we worked through these results. Our thanks also go to R. Schoof for his encouragement and suggestions, as well as to our anonymous (but inva
In this paper we prove several theorems about abelian varieties over finite fields by studying the set of monic real polynomials of degree 2n all of whose roots lie on the unit circle. In particular, we consider a set V n of vectors in R n that give the coefficients of such polynomials. We calculate