637 research outputs found
Hyodo--Kato theory with syntomic coefficients
The purpose of this article is to establish theories concerning -adic
analogues of Hodge cohomology and Deligne--Beilinson cohomology with
coefficients in variations of mixed Hodge structures. We first study log
overconvergent -isocrystals as coefficients of Hyodo--Kato cohomology. In
particular, we prove a rigidity property of Hain--Zucker type for mixed log
overconvergent -isocrystals. In the latter half of the article, we give a
new definition of syntomic coefficients as coefficients of -adic Hodge
cohomology and syntomic cohomology, and prove some fundamental properties
concerning base change and admissibility. In particular, we see that our
framework of syntomic coefficients depends only on the choice of a branch of
the -adic logarithm, but not on the choice of a uniformizer of the base
ring. The rigid analytic reconstruction of Hyodo--Kato map studied by Ertl and
the author plays a key role throughout this article.Comment: 2nd version, 72 pages. I fixed a mistake concerning dependence of
pseudo-constant syntomic coefficient on the choice of uniformizer. To do
this, I slightly modified the definition of pseudo-constant log
overconvergent isocrystal (Definition 3.8), newly introduced "twist" of Hodge
structure (Definition 9.8), and fixed the statement for the compatibility
with base change (Proposition 9.9
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