We prove the perfectness of Grothendieck's pairing on l-parts of component groups of an abelian variety and its dual when l is prime to the residue characteristic. We show that this pairing differs in sign from another perfect pairing introduced by Grothendieck.
On perfectness of Grothendieck's pairing for the l-parts of component groups
BERTAPELLE, ALESSANDRA
2001
Abstract
We prove the perfectness of Grothendieck's pairing on l-parts of component groups of an abelian variety and its dual when l is prime to the residue characteristic. We show that this pairing differs in sign from another perfect pairing introduced by Grothendieck.
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