22 citations · 38 across the 19 of their papers we have counts for
19 papers
Logarithmic geometry and Frobenius, II
Kazuya Kato, Chikara Nakayama, Sampei Usui
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 an…
Logarithmic Tate conjectures over finite fields
Kazuya Kato, Chikara Nakayama, Sampei Usui
We formulate an analogue of Tate conjecture on algebraic cycles, for the log geometry over a finite field. We show that the weight-monodromy conjecture follows from this conjecture…
Logarithmic geometry and Frobenius
Kazuya Kato, Chikara Nakayama, Sampei Usui
Based on the logarithmic algebraic geometry and the theory of Deligne systems, we define an abelian category of -adic sheaves with weight filtrations on a logarithmic scheme…
Classifying spaces of degenerating mixed Hodge structures, VI: Log real analytic functions and log functions
Kazuya Kato, Chikara Nakayama, Sampei Usui
To advance our log Hodge theory, we introduce log real analytic functions and log functions, define how to integrate them, and prove the log Poincaré lemma. We give be…
Mixed objects are embedded into log pure objects
Kazuya Kato, Chikara Nakayama, Sampei Usui
We prove that a variation of mixed Hodge structure is embedded in a logarithmic variation of pure Hodge structure, and a generalized version of this result. These results suggest s…
Deligne--Beilinson cohomology and log Hodge theory
Kazuya Kato, Chikara Nakayama, Sampei Usui
We show that the description of Deligne--Beilinson cohomology is improved by using log Hodge theory. We consider the log relative version of it, and also present a fundamental conj…