A note on the first rigid cohomology group for geometrically unibranch varieties

Nobuo Tsuzuki

doi:10.4171/rsmup/128-3

A note on the first rigid cohomology group for geometrically unibranch varieties

Nobuo Tsuzuki

SCI - Mathematics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	3
Number of pages	1
Journal	Rendiconti del Seminario Matematico dell 'Universita' di Padova/Mathematical Journal of the University of Padova
Volume	128
DOIs	https://doi.org/10.4171/rsmup/128-3
Publication status	Published - 2012

ASJC Scopus subject areas

Analysis
Algebra and Number Theory
Mathematical Physics
Geometry and Topology

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