The monodromy pairing for logarithmic 1-motifs
Algebraic Geometry
2023-01-18 v2
Abstract
We describe a 3-step filtration on all logarithmic abelian varieties with constant degeneration. The obstruction to descending this filtration, as a variegated extension, from logarithmic geometry to algebraic geometry is encoded in a bilinear pairing valued in the characteristic monoid of the base. This pairing is realized as the monodromy pairing in p-adic, l-adic, and Betti cohomolgies, and recovers the Picard-Lefschetz transformation in the case of Jacobians. The Hodge realization of the filtration is the monodromy weight filtration on the limit mixed Hodge structure.
Keywords
Cite
@article{arxiv.1912.04253,
title = {The monodromy pairing for logarithmic 1-motifs},
author = {Jonathan Wise},
journal= {arXiv preprint arXiv:1912.04253},
year = {2023}
}
Comments
40 pages; this version contains many corrections, as well as new sections about logarithmic tori and duality for logarithmic 1-motifs; comments welcome!