Reduction of Abelian Varieties and Grothendieck’s Pairing

  • Klaus Loerke
  • Published 2009

Abstract

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. 

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