We study equivariant deformations of singular curves with an action of a finite flat group scheme, using a simplified version of Illusie’s equivariant cotangent complex. We apply these methods in a special case which is relevant for the study of the stable reduction of three point covers.
Nous étudions les déformations équivariantes d’une courbe singulière sur laquelle agit un schéma en groupes, en utilisant une version simplifiée du complexe cotangent équivariant définie par Illusie. Ces méthodes sont explicitées dans un cas particulier qui apparaît naturellement dans l’étude des revêtements galoisiens étale de la droite projective moins trois points.
Classification: 14B12, 14H30, 13D10
Keywords: Equivariant deformation, curves, group schemes, cotangent complex
@article{AIF_2005__55_4_1105_0, author = {Wewers, Stefan}, title = {Formal deformation of curves with group scheme action}, journal = {Annales de l'Institut Fourier}, pages = {1105--1165}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {55}, number = {4}, year = {2005}, doi = {10.5802/aif.2122}, mrnumber = {2157165}, zbl = {1079.14006}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2122/} }
TY - JOUR TI - Formal deformation of curves with group scheme action JO - Annales de l'Institut Fourier PY - 2005 DA - 2005/// SP - 1105 EP - 1165 VL - 55 IS - 4 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2122/ UR - https://www.ams.org/mathscinet-getitem?mr=2157165 UR - https://zbmath.org/?q=an%3A1079.14006 UR - https://doi.org/10.5802/aif.2122 DO - 10.5802/aif.2122 LA - en ID - AIF_2005__55_4_1105_0 ER -
Wewers, Stefan. Formal deformation of curves with group scheme action. Annales de l'Institut Fourier, Volume 55 (2005) no. 4, pp. 1105-1165. doi : 10.5802/aif.2122. https://aif.centre-mersenne.org/articles/10.5802/aif.2122/
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