We studied the crystalline nature of the universal extension of a 1-motive, over a general basis, in order to define a Gauss-Manin connectionon the de Rham realization of a 1-motive. This construction generalizes the classical one for abelian schemes. As an application we gave a motivic interpretation of the Manin map introduced by Manin in the proof of Mordell conjecture for abelian varieties over function fields of characteristic 0.
UNIVERSAL EXTENSION CRYSTALS OF 1-MOTIVES AND APPLICATIONS
BERTAPELLE, ALESSANDRA
2011
Abstract
We studied the crystalline nature of the universal extension of a 1-motive, over a general basis, in order to define a Gauss-Manin connectionon the de Rham realization of a 1-motive. This construction generalizes the classical one for abelian schemes. As an application we gave a motivic interpretation of the Manin map introduced by Manin in the proof of Mordell conjecture for abelian varieties over function fields of characteristic 0.
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