Logarithmic geometry and Frobenius, II
Kazuya Kato, Chikara Nakayama, Sampei Usui
TL;DR
This paper explores the analogy between log mixed Hodge structures and $ ext{ell}$-adic categories, proving $ ext{ell}$-adic versions of key theorems in Hodge theory related to the SL(2)-orbit theorem.
Contribution
It introduces $ ext{ell}$-adic analogues of classical Hodge theory theorems, advancing the understanding of the weight-monodromy conjecture in this context.
Findings
Proved $ ext{ell}$-adic analogues of Hodge theory theorems
Established connections between log mixed Hodge structures and $ ext{ell}$-adic categories
Contributed to the understanding of the weight-monodromy conjecture
Abstract
Based on the strong analogy between the category of log mixed Hodge structures and the category of -adic nature, which we have introduced in the previous part and is closely related to the weight-monodromy conjecture, we prove the -adic analogues of some theorems in Hodge theory related to the SL(2)-orbit theorem.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Homotopy and Cohomology in Algebraic Topology · Advanced Algebra and Geometry