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$\begingroup$ Great! The minus sign that intervenes here is a good cautionary tale: not all naturally-defined pairings are the same as one another. In any case, the instance I care about is in characteristic zero, so I will accept this answer. $\endgroup$

Alexander Betts
– Alexander Betts

2021-05-15 15:34:37 +00:00
Commented May 15, 2021 at 15:34
$\begingroup$ This is the same minus sign as that in Section 24, Theorem 1, of Mumford's book on Abelian Varieties (over the complex numbers). $\endgroup$

user166831
– user166831

2021-05-16 12:31:50 +00:00
Commented May 16, 2021 at 12:31

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