p-Adic Heights on Abelian Varieties

  • Yuri G. Zarhin
Part of the Progress in Mathematics book series (PM, volume 22)


It has recently become clear that the construction of a p-adic height on an Abelian variety A eventually reduces to a splitting of the Hodge filtration of its de Rham cohomology. The present paper provides a natural description of this connection, based on the study of the universal vectorial extension of A , and of rigidified extensions of algebraic groups. Following a request of the editor, a detailed introduction to these topics has been included, in order to make the text as self-contained as possible.


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Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • Yuri G. Zarhin
    • 1
  1. 1.Research Computing CenterThe USSR Academy of SciencesPushchino Moscow RegionUSSR

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