ROCHER, Magali

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ROCHER, Magali
Institut de Mathématiques de Bordeaux [IMB]

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Journal of Algebra. 2009, vol. 321, n° 2, p. 704-740

Elsevier

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Let $k$ be an algebraically closed field of characteristic $p>0$ and $C$ a connected nonsingular projective curve over $k$ with genus $g \geq 2$. Let $(C,G)$ be a "big action" , i.e. a pair $(C,G)$ where $G$ is a $p$-subgroup of the $k$-automorphism group of $C$ such that$\frac{|G|}{g} >\frac{2\,p}{p-1}$. We denote by $G_2$ the second ramification group of $G$ at the unique ramification point of the cover $C \rightarrow C/G$. The aim of this paper is to describe the big actions whose $G_2$ is $p$-elementary abelian. In particular, we obtain a structure theorem by considering the $k$-algebra generated by the additive polynomials. We more specifically explore the case where there is a maximal number of jumps in the ramification filtration of $G_2$. In this case, we display some universal families.< Réduire

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Large p-group actions with a p-elementary abelian derived group.

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