Rendiconti del Seminario Matematico della Università di Padova
Full-Text PDF (648 KB) | Metadata | Table of Contents | RSMUP summary
A Note on the First Rigid Cohomology Group for Geometrically Unibranch VarietiesNobuo Tsuzuki (1) Mathematical Institute, Tohoku University, Aramaki Aza-Aoba 6-3, Aobaku, 980-8578, Sendai, Japan
We prove a vanishing of the first rigid cohomology group for geometrically unibranch varieties with supports in a proper closed subset and apply it to the full faithfulness problem of the restriction functors of overconvergent isocrystals. As an application, we prove that the first rigid cohomology group is pure of weight 1 for proper and geometrically unibranch varieties over a finite field. We also establish a comparison result of rigid cohomology groups between a geometrically unibranch variety and its normalization.
No keywords available for this article.
Tsuzuki Nobuo: A Note on the First Rigid Cohomology Group for Geometrically Unibranch Varieties. Rend. Sem. Mat. Univ. Padova 128 (2012), 17-53. doi: 10.4171/RSMUP/128-3