✦ LIBER ✦
Rational Points on Picard Groups of Some Genus-Changing Curves of Genus at Least 2
✍ Scribed by Sangtae Jeong
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 163 KB
- Volume
- 89
- Category
- Article
- ISSN
- 0022-314X
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✦ Synopsis
For an algebraic curve CÂK defined by y 2 =x p +a (a  K p ) with relative genus ( p&1)Â2 and absolute genus 0, we prove that the Picard group of divisors of degree 0, denoted Pic 0 K (C), of a curve CÂK fixed by the action of the Galois group G= gal(K sep ÂK) has a finite number of K-rational points as a variety, where K is a function field in one variable with a finite constant field of characteristic p 5 and K sep is the separable closure of K.