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Supersingular Curves of Genus 2 over Finite Fields of Characteristic 2

✍ 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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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

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We show that SK 1 X = 0 for every affine curve X over a finite field.

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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 Þ the vector space of 2 Γ‚ 2-matrices over F. The group GLΓ°2; FÞ acts on Mat 2;2 Γ°F q Þ by conjugation. In this note, we determine the invariants of this action. In contrast to the case of an infinite field, where

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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