Let $C$ be an algebraic projective smooth and trigonal curve of genus $g\ge 5$. In this paper we define, in a way equivalent to that followed by A. Maroni in [1], an integer $m$, called the species of $C$, which is a birational invariant having the property that $0\le m\le \frac{g+2}{3}$ and $m\mathrm{—}g\equiv 0$ mod(2). In section 1 we prove that for every $g(\ge 5)$ and every $m$, as before, there are trigonal curves of genus $g$ and species $m$. In section 2 we define the space ${ℳ}_{g,3;m}^1$ of moduli of trigonal curves of genus $g$ and species $m$. We note that ${ℳ}_{g,3;m}^1$ is irreducible...

Nous étudions les espaces analytiques rigides de dimension 1, réguliers, de genre fini sur un corps valué complet $k$. Nous montrons qu’un tel espace $X$ admet une réduction préstable. Si $k$ est maximalement complet, $X$ se plonge dans une courbe algébrique (analytifiée). On donne aussi une caractérisation des espaces analytiques qui sont le complémentaire d’une partie compacte dans une courbe algébrique.

The goal of this work is to construct, for a smooth variety $X$ over a perfect field k of finite characteristic $p\>0$, an overconvergent de Rham-Witt complex $W^{†}{\Omega }_{X/k}$ as a suitable subcomplex of the de Rham-Witt complex of Deligne-Illusie. This complex, which is functorial in $X$, is a complex of étale sheaves and a differential graded algebra over the ring $W^{†}\left({𝒪}_X\right)$ of overconvergent Witt-vectors. If $X$ is affine one proves that there is an isomorphism between Monsky-Washnitzer cohomology and (rational) overconvergent...

2000 Mathematics Subject Classification: 12D10.In the paper we give different examples of overdetermined strata.