On p-adic differential equations on semistable varieties II
Di Proietto, V
This paper is a complement to the paper "On p-adic differential equations on semistable varieties" written by V. Di Proietto. Given an open variety over a DVR with semistable reduction, the author constructed in that paper a fully faithful algebraization functor from the category of certain log overconvergent isocrystals on the special fiber to the category of modules with regular integrable connection on the generic fiber. In this paper, we prove that, with convenable hypothesis, this functor is a tensor functor whose essential image is closed under extensions and subquotients. As a consequence, we can find suitable Tannakian subcategories of log overconvergent isocrystals and of modules with regular integrable connection on which the algebraization functor is an equivalence of Tannakian categories.
The main part of this work was done when the first author was at the Graduate School of Mathematical Sciences of the University of Tokyo supported by a postdoctoral fellowship and kaken-hi (grant-in-aid) of the Japanese Society for the Promotion of Science (JSPS). She is now supported by a postdoctoral fellowship of Labex IRMIA.When the main part of this work was done, the second author was supported by JSPS Grant-in-Aid for Young Scientists (B) 21740003 and Grant-in-Aid for Scientific Research (B) 22340001. Currently he is supported by JSPS Grant-in-Aid for Scientific Research (C) 25400008 and Grant-in-Aid for Scientific Research (B) 23340001.
This is the author accepted manuscript. The final version is available from Springer Verlag via the DOI in this record.
Vol. 146, Issue 1, pp 179–199