Searcharxiv⌕ Search

arXiv subjects

Klaus Loerke

Publications and source records attributed to Klaus Loerke.

2 recordsLinked to original sources
arXiv2009

Cup Products and Pairings for Abelian Varieties

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.

math.AG↗
arXiv2009

Reduction of Abelian Varieties and Grothendieck's Pairing

We prove that abelian varieties of small dimension over discrete valuated, stricty henselian ground fields with perfect residue class field obtain semistable reduction after a tamely ramified extension of the ground field. Using this result we obtain perfectness results for Grothendieck's pairing.

math.AG↗