2017/04/06 by Stefan Schröer, Schröer, Stefan, Yukihide Takayama +1
Mathematics · #14B25 #14D15 #14F17 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1704.01725
openalex publication_date 2017/04/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Using the set-up of deformation categories of Talpo and Vistoli, we re-interpret and generalize, in the context of cartesian morphisms in abstract categories, some results of Rim concerning obstructions against extensions of group actions in infinitesimal deformations. Furthermore, we observe that finite étale coverings can be infinitesimally extended and the resulting formal scheme is algebraizable. Finally, we show that pre-Tango structures survive under pullbacks with respect to finite, generically étale surjections π:X→ Y, and record some consequences regarding Kodaira vanishing in degree one.