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Buium-Manin theory and periods of Abelian varieties Katz, Eric
Description
An important tool for bounding the number of rational or torsion points on a curve is to find a function that vanishes at those points and bounding its zeroes. This is essential to Coleman's effective Chabauty and Buium's p-adic differential characters. Buium's work, while appearing quite different, is based on Manin's proof of the function field Mordell conjecture which made use of a Picard-Fuchs differential operator annihilating the periods of an Abelian variety. In this talk, we will discuss a project with Dupuy, Rabinoff, and Zureick-Brown to unify Buium's and Coleman's work in hope of finding more functions vanishing on points of arithmetic interest. This involves constructing differential characters using the p-adic integration theories of Coleman and Colmez, understanding the periods of Abelian varieties, and connections with p-adic Hodge theory.
Item Metadata
Title |
Buium-Manin theory and periods of Abelian varieties
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2017-06-02T09:00
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Description |
An important tool for bounding the number of rational or torsion points on a curve is to find a function that vanishes at those points and bounding its zeroes. This is essential to Coleman's effective Chabauty and Buium's p-adic differential characters. Buium's work, while appearing quite different, is based on Manin's proof of the function field Mordell conjecture which made use of a Picard-Fuchs differential operator annihilating the periods of an Abelian variety. In this talk, we will discuss a project with Dupuy, Rabinoff, and Zureick-Brown to unify Buium's and Coleman's work in hope of finding more functions vanishing on points of arithmetic interest. This involves constructing differential characters using the p-adic integration theories of Coleman and Colmez, understanding the periods of Abelian varieties, and connections with p-adic Hodge theory.
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Extent |
45 minutes
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: Ohio State University
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Series | |
Date Available |
2017-11-30
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0360789
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Faculty
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International