Abstract:
After discussing gradings by sheaves of degrees, we associate to any log scheme a canonical invertible sheaf endowed with a certain multiplicative structure, which we call its associated graded algebra. In the relative case we construct a canonical connection on this algebra. In the log smooth case over a base of positive characteristic p, we study integrable and p-integrable graded modules over this algebra, and establish a Cartier type p-descent theorem, generalizing previous results of Ogus. We apply it to give an alternate proof of a result of Tsuji on closed forms fixed by the Cartier operator
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Received: 15 January 1999 / Revised version: 30 September 1999
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Lorenzon, P. Indexed algebras associated to a log structure and a theorem of p-descent on log schemes. manuscripta math. 101, 271–299 (2000). https://doi.org/10.1007/s002290050216
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DOI: https://doi.org/10.1007/s002290050216