✦ LIBER ✦
Galois Groups of Unramified Covers of Projective Curves in Characteristicp
✍ Scribed by Katherine F. Stevenson
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 414 KB
- Volume
- 182
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
✦ Synopsis
We show several results concerning the finite groups that occur as Galois groups of unramified covers of projective curves in characteristic p. In particular, we prove that every finite group with g generators occurs over some curve of genus g. This implies, for example, that every finite simple group occurs in genus 2. By similar methods, we obtain several other families of groups which occur in genus 2. In addition, we show that if a group G occurs over some curve of genus g, then it must occur over ''almost all'' curves of genus g or greater. The results are obtained using formal patching.