Abstract
This paper is a complement to the paper “On p-adic differential equations on semistable varieties” by 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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
André, Y., Baldassarri, F.: De Rham Cohomology of Differential Modules on Algebraic Varieties. Progress in Mathematics, vol. 189. Birkhäuser, Basel (2001)
Baldassarri F.: Towards an algebraic proof of Deligne’s regularity criterion. An informal survey of open problems. Milan J. Math. 73, 237–258 (2005)
Baldassarri F., Chiarellotto B.: Formal and p-adic theory of differential systems with logarithmic singularities depending upon parameters. Duke Math. J. 72(1), 241–300 (1993)
Berthelot, P.: Cohomologie rigide et cohomologie rigide à support propre. Première partie. prépublication de l’IRMAR 96-03 (1996)
Deligne, P.: Equations différentielles à points singuliers réguliers. In: Lecture Notes in Mathematics, vol. 163. Springer, Berlin (1970)
Deligne P.: Catégories tannakiennes, The Grothendieck Festschrift, Vol II, Progress in Mathematics, vol. 87, pp. 111–195. Birkhäuser Boston, Boston (1990)
Deligne, P., Milne, J.S.: Tannakian categories. Hodge cycles, motives, and Shimura varieties. In: Deligne, P., Milne, J.S., Ogus, A., Shih, K. (eds.) Lecture Notes in Mathematics, vol. 900. Springer, Berlin, pp. 101–228 (1982)
Di Proietto V.: On p-adic differential equations on semistable varieties. Math. Z. 274, 1047–1091 (2013)
Kedlaya K.S.: Semistable reduction for overconvergent F-isocrystals. I. Unipotence and logarithmic extensions. Compositio Math. 143(5), 1164–1212 (2007)
Shiho A.: Crystalline fundamental groups. I. Isocrystals on log crystalline site and log convergent site. J. Math. Sci. Univ. Tokyo 7(4), 509–656 (2000)
Shiho, A.: Relative log convergent cohomology and relative rigid cohomology II. arXiv:0707.1743
Shiho A.: Cut-by-curves criterion for the overconvergence of p-adic differential equations. Manuscripta Math. 132(3–4), 517–537 (2010)
Shiho A.: On logarithmic extension of overconvergent isocrystals. Math. Ann. 348, 467–512 (2010)
Shiho, A.: Parabolic log convergent isocrystals. arXiv:1010.4364
Shiho A.: Cut-by-curves criterion for the log extendability of overconvergent isocrystals. Math. Z. 269(1–2), 59–82 (2011)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Di Proietto, V., Shiho, A. On p-adic differential equations on semistable varieties II. manuscripta math. 146, 179–199 (2015). https://doi.org/10.1007/s00229-014-0691-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00229-014-0691-9