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The monodromy pairing
for logarithmic $1$-motifs
Jonathan Wise |
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Vol. 4 (2022), No. 4, 587–633
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Abstract |
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We describe a -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 -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. |
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Keywords
logarithmic geometry, abelian varieties, tropical geometry,
monodromy pairing
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Mathematical Subject Classification 2010
Primary: 14C22, 14D07, 14F42, 14H40, 14K05
Secondary: 14T05
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Milestones
Received: 24 March 2020
Revised: 8 June 2022
Accepted: 28 June 2022
Published: 15 January 2023
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Authors |
| Jonathan Wise | |
| Department of Mathematics University of Colorado Boulder, CO United States |
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