Download this article
Download this article For screen
For printing
Recent Issues
Volume 6, Issue 2
Volume 6, Issue 1
Volume 5, Issue 4
Volume 5, Issue 3
Volume 5, Issue 2
Volume 5, Issue 1
Volume 4, Issue 4
Volume 4, Issue 3
Volume 4, Issue 2
Volume 4, Issue 1
Volume 3, Issue 4
Volume 3, Issue 3
Volume 3, Issue 2
Volume 3, Issue 1
Volume 2, Issue 4
Volume 2, Issue 3
Volume 2, Issue 2
Volume 2, Issue 1
Volume 1, Issue 4
Volume 1, Issue 3
Volume 1, Issue 2
Volume 1, Issue 1
The Journal
About the journal
Ethics and policies
Peer-review process
Statement, 2023
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN (electronic): 2576-7666
ISSN (print): 2576-7658
Author index
To appear
 
Other MSP Journals
The monodromy pairing for logarithmic $1$-motifs

Jonathan Wise

Vol. 4 (2022), No. 4, 587–633
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, -adic, and Betti cohomologies, 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
logarithmic geometry, abelian varieties, tropical geometry, monodromy pairing
Mathematical Subject Classification 2010
Primary: 14C22, 14D07, 14F42, 14H40, 14K05
Secondary: 14T05
Milestones
Received: 24 March 2020
Revised: 8 June 2022
Accepted: 28 June 2022
Published: 15 January 2023
Authors
Jonathan Wise
Department of Mathematics
University of Colorado
Boulder, CO
United States