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arXiv · 0909.3940

Cup Products and Pairings for Abelian Varieties

Klaus Loerke
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Abstract

Let $A_K$ be an abelian variety with semistable reduction over a strictly henselian field of positive characteristic with perfect residue class field. We show that there is a close connection between the pairings of Grothendieck, Bester/Bertapelle and Shafarevic. In particular, we show that the pairing of Bester/Bertapelle can be used to describe the $p$-part of Grothendieck's pairing in the semistable reduction case, thus proving a conjecture of Bertapelle.

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Klaus Loerke. 2009-09-24. Cup Products and Pairings for Abelian Varieties. https://arxiv.org/abs/0909.3940

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