The $l$-adic El Zein-Steenbrink-Zucker bifiltered complex of a projective SNCL scheme with a relative SNCD
Yukiyoshi Nakkajima
Published: 2025/3/31
Abstract
For a family of log points with constant log structure and for a proper SNCL scheme with an SNCD over the family, we construct a fundamental l-adic bifiltered complex as a geometric application of the theory of the derived category of (bi)filtered complexes in our papers. By using this bifiltered complex, we give the formulation of the log l-adic relative monodromy-weight conjecture with respect to the filtration arising from the SNCD. That is, we state that the relative l-adic monodromy filtration should exist for the Kummer log etale cohomological sheaf of the proper SNCL scheme with an SNCD and it should be equal to the l-adic weight filtration.