On maximal curves in characteristic two
✍ Scribed by Miriam Abdón; Fernando Torres
- Publisher
- Springer
- Year
- 1999
- Tongue
- English
- Weight
- 96 KB
- Volume
- 99
- Category
- Article
- ISSN
- 0025-2611
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We study arithmetical and geometrical properties of maximal curves, that is, curves defined over the finite field F q 2 whose number of F q 2 -rational points reaches the Hasse Weil upper bound. Under a hypothesis on non-gaps at a rational point, we prove that maximal curves are F q 2 -isomorphic to
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