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Local heights on abelian varieties with split multiplicative reduction

Published online by Cambridge University Press:  04 December 2007

ANNETTE WERNER
ANNETTE WERNER
Affiliation:
Mathematisches Institut, Universität Münster, Einsteinstr, 62, D-48149 Münster; e-mail: werner@math.uni-muenster.de
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Abstract

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We express Néron functions and Schneider's local $p$-adic height pairing on an abelian variety $A$ with split multiplicative reduction with theta functions and their automorphy factors on the rigid analytic torus uniformizing $A$. Moreover, we show formulas for the $\rho$-splittings of the Poincaré biextension corresponding to Néron's and Schneider's local height pairings.

Keywords

Néron functions$p$-adic height pairingsrigid analytic uniformizationtheta functions
Type
Research Article
Information
Compositio Mathematica , Volume 107 , Issue 3 , July 1997 , pp. 289 - 317
Copyright
© 1997 Kluwer Academic Publishers