The l-adic bifiltered El Zein-Steenbrink-Zucker complex of a proper SNCL scheme with a relative SNCD

2025/03/31 by Nakkajima, Yukiyoshi
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2504.00201

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.

Related

• The zariskian p-adic bifiltered El Zein-Steenbrink-Zucker complex of a proper SNCL scheme with a relative SNCD
• Theory of weights for log convergent cohomologies II: the case of a proper SNCL scheme in characteristic p>0
• Theory of weights for log convergent cohomologies I: the case of a proper smooth scheme with an SNCD in characteristic p>0
• Logarithmic geometry and Frobenius
• Hirsch weight-filtered log crystalline complex and Hirsch weight-filtered log crystalline dga of a proper SNCL scheme in characteristic p>0