19 research outputs found
Derived PD-Hirsch extensions of filtered crystalline complexes and filtered crysalline dga's
We construct a theory of the derived PD-Hirsch extension of the log
crystalline complex of a log smooth scheme and we construct a fundamental
filtered dga and a fundamental filtered complex
for a simple normal crossing log scheme over a family of
log points by using the log crystalline method in order to overcome obstacles
arising from the incompatibility of the p-adic Steenbrink complexes in [M] and
[Nak4] with the cup product of the log crystalline complex of . When the
base log scheme is the log point of a perfect field of characteristic , we
prove that and is canonically
isomorphic to Kim and Hain's filtered dga and their filtered complex in [KH],
respectively.Comment: 156 pages. arXiv admin note: text overlap with arXiv:1902.0018
Degenerations of log Hodge de Rham spectral sequences, log Kodaira vanishing theorem in characteristic and log weak Lefschetz conjecture for log crystalline cohomologies
In this article we prove that the log Hodge de Rham spectral sequences of
certain proper log smooth schemes of Cartier type in characteristic
degenerate at . We also prove that the log Kodaira vanishings for them
hold when they are projective. We formulate the log weak Lefschetz conjecture
for log crystalline cohomologies and prove that it is true in certain cases.Comment: 74 page
Weight-filtered convergent complex
Using log convergent topoi, %In the derived category of filtered complexes of
%sheaves of modules over %an isostructure we define two fundamental filtered
complexes and for the log scheme obtained by a
smooth scheme with a relative simple normal crossing divisor over a scheme of
characteristic . Using , we prove the -adic purity. As a
corollary of it, we prove that and are
canonically isomorphic. These filtered complexes produce the weight spectral
sequence of the log convergent cohomology sheaf of the log scheme. We also give
the comparison theorem between the projections of and
to the derived category of bounded below filtered complexes of
sheaves of modules in the Zariski topos of the log scheme and the
weight-filtered isozariskian filtered complex of the log
scheme defined in our previous book.Comment: 83page