On extension of overconvergent log isocrystals on log smooth varieties

Abstract

By works of Kedlaya and Shiho, it is known that, for a smooth variety X over a field of positive characteristic and its simple normal crossing divisor Z, an overconvergent isocrystal on the compliment of Z satisfying a certain monodromy condition can be extended to a convergent log isocrystal on X, M Z , where M Z is the log structure associated to Z. We prove a generalization of this result: for a log smooth variety X, M satisfying some conditions, an overconvergent log isocrystal on the trivial locus of a direct summand of M satisfying a certain monodromy condition can be extended to a convergent log isocrystal on X, M . r i=1 Σ i , if E has Σ i -unipotent along Z i for each 1991 Mathematics Subject Classification. 12H25.