The class group of a one-dimensional affinoid space
Annales de l'institut Fourier (1980)
- Volume: 30, Issue: 4, page 155-164
- ISSN: 0373-0956
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topPut, Marius Van Der. "The class group of a one-dimensional affinoid space." Annales de l'institut Fourier 30.4 (1980): 155-164. <http://eudml.org/doc/74469>.
@article{Put1980,
abstract = {A curve $X$ over a non-archimedean valued field is with respect to its analytic structure a finite union of affinoid spaces. The main result states that the class group of a one dimensional, connected, regular affinoid space $Y$ is trivial if and only if $Y$ is a subspace of $\{\bf P\}^1$. As a consequence, $X$ has locally a trivial class group if and only if the stable reduction of $X$ has only rational components.},
author = {Put, Marius Van Der},
journal = {Annales de l'institut Fourier},
keywords = {curve over a non-archimedean valued field; class group of a one-dimensional connected regular affinoid space; trivial class group},
language = {eng},
number = {4},
pages = {155-164},
publisher = {Association des Annales de l'Institut Fourier},
title = {The class group of a one-dimensional affinoid space},
url = {http://eudml.org/doc/74469},
volume = {30},
year = {1980},
}
TY - JOUR
AU - Put, Marius Van Der
TI - The class group of a one-dimensional affinoid space
JO - Annales de l'institut Fourier
PY - 1980
PB - Association des Annales de l'Institut Fourier
VL - 30
IS - 4
SP - 155
EP - 164
AB - A curve $X$ over a non-archimedean valued field is with respect to its analytic structure a finite union of affinoid spaces. The main result states that the class group of a one dimensional, connected, regular affinoid space $Y$ is trivial if and only if $Y$ is a subspace of ${\bf P}^1$. As a consequence, $X$ has locally a trivial class group if and only if the stable reduction of $X$ has only rational components.
LA - eng
KW - curve over a non-archimedean valued field; class group of a one-dimensional connected regular affinoid space; trivial class group
UR - http://eudml.org/doc/74469
ER -
References
top- [1] A. ESCASSUT, Éléments spectralement injectifs et générateurs universels dans une algèbre de Tate, Memoria publicada en Collectanea Mathematica vol. XXVIII, fasc. 2 (1977), 131-148. Zbl0389.12012MR58 #22658
- [2] L. GERRITZEN, M. van der PUT, p-adic Schottky groups and Mumford curves, forthcoming in Lecture Notes in Math.
- [3] M. van der PUT, Schottky groups and Schottky curves, Algebraic Geometry, 1978, Lecture Notes in Math., 732, 518-526. Zbl0412.14023MR82a:14007
Citations in EuDML Documents
top- Q. Liu, Ouverts analytiques d'une courbe algébrique en géométrie rigide
- Jean Fresnel, Marius Van Der Put, Localisation formelle et groupe de Picard
- Qing Liu, Ouverts analytiques d'une courbe algébrique en géométrie rigide
- M. Van der Put, Cohomology on affinoid spaces
- Vladimir G. Berkovich, Étale cohomology for non-Archimedean analytic spaces
- Marius Van der Put, De Rham cohomology of affinoid spaces
- Jean Fresnel, Marius van der Put, Uniformisation des variétés abéliennes
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