Supersingular Curves of Genus 2 over Finite Fields of Characteristic 2
β Scribed by Gerard Van Der Geer; Marcel Van Der Vlugt
- Publisher
- John Wiley and Sons
- Year
- 1992
- Tongue
- English
- Weight
- 396 KB
- Volume
- 159
- Category
- Article
- ISSN
- 0025-584X
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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
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 clas
We show that SK 1 X = 0 for every affine curve X over a finite field.
Let F q be the finite field with q elements, q ΒΌ p n ; p 2 N a prime, and Mat 2:2 Γ°F q Γ the vector space of 2 Γ 2-matrices over F. The group GLΓ°2; FΓ acts on Mat 2;2 Γ°F q Γ by conjugation. In this note, we determine the invariants of this action. In contrast to the case of an infinite field, where
Using Drinfeld modular curves we determine the places of supersingular reduction of elliptic curves over F 2 r( T) with certain conductors. This enables us to classify and describe explicitly all elliptic curves over F 2 r( T ) having a conductor of degree 4. Our results also imply that extremal ell