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Complex valued Néron-Tate height pairings

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Speaker: 
Gerard Freixas i Montplet
Affiliation: 
Inst. de Math. de Jussieu, Paris
Date: 
Wed, 2017-02-08 14:15 - 15:15
Location: 
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

Néron-Tate height pairings are defined on jacobians of curves over number fields. The jacobian admits the so-called universal vector extension, the moduli of line bundles with connections. I will describe an attempt to extent the Néron-Tate pairing to the universal vector extension, and the relation to the complex valued analytic torsion introduced by Cappell-Miller. The link betweem both is a Riemann-Roch type formula in Arakelov geometry, a variant of Kronecker's second limit formula.

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