2025/02/24 by Kazuya Kato, Kato, Kazuya, Chikara Nakayama +3
Computer Science · Mathematics · #19E15 #Algebraic Geometry (math.AG) #Analytic Number Theory Research #Coding theory and cryptography #FOS: Mathematics #Limits and Structures in Graph Theory #Primary 14A21 #Secondary 14F20
paper · pdf · doi:10.48550/arxiv.2502.16974
openalex publication_date 2025/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 and from the semi-simplicity of the Frobenius action. This conjecture suggests the existence of the monodromy cycle which gives the monodromy operator and an action of \fraksl(2) on the cohomology, and which lives in the world of log motives.