Mathematical Research Letters

Volume 24 (2017)

Number 6

Overconvergent unit-root $F$-isocrystals and isotriviality

Pages: 1707 – 1727



Teruhisa Koshikawa (Department of Mathematics, University of Chicago, Illinois, U.S.A.; and Research Institute for Mathematical Sciences, Kyoto University, Kyoto, Japan)


We show that a semisimple overconvergent “absolutely unit-root” $F$-isocrystal on a geometrically connected smooth variety over a finite field becomes constant over a finite covering.

Received 30 January 2016

Accepted 3 June 2016

Published 29 January 2018