On holomorphic polydifferentials in positive characteristic
| Autor: | Sotiris Karanikolopoulos |
|---|---|
| Rok vydání: | 2012 |
| Předmět: |
14H37
11G20 Pure mathematics Mathematics - Number Theory G-module General Mathematics Galois group Field (mathematics) Elementary abelian group Mathematics - Algebraic Geometry FOS: Mathematics Order (group theory) Number Theory (math.NT) Galois extension Abelian group Algebraic Geometry (math.AG) Function field Mathematics |
| Zdroj: | Mathematische Nachrichten. 285:852-877 |
| ISSN: | 0025-584X |
| Popis: | In this paper we study the space $\Omega(m)$, of holomorphic $m$-(poly)differentials of a function field of a curve defined over an algebraically closed field of characteristic $p>0$ when $G$ is cyclic or elementary abelian group of order $p^n$; we give bases for each case when the base field is rational, introduce the Boseck invariants and give an elementary approach to the $G$ module structure of $\Omega(m)$ in terms of Boseck invariants. The last computation is achieved without any restriction on the base field in the cyclic case, while in the elementary abelian case it is assumed that the base field is rational. An application to the computation of the tangent space of the deformation functor of curves with automorphisms is given. Comment: 25 pages, corrected typos, changes in presentation, a closed formula for the calculation in section 5, 2 case is added |
| Databáze: | OpenAIRE |
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