2
$\begingroup$

Let $X$ be a curve over some algebraically closed field $k$ and let $J$ be its Jacobian. I have read that one should think of the Tate module $T_lJ$ as being the first homology group of $X$ with coefficients on $\mathbb{Z}_l$.

Now in the classical case an important tool is to integrate differentials along elements of the homology group with integral coefficients. Is there anything similar one can do with differentials on $X$ and elements of the Tate module of $J$?

Improve this question
$\endgroup$
2
  • 2
    $\begingroup$ If the field in question is $\ell$-adic, one can do this with $p$-adic Hodge theory. $\endgroup$
    – Will Sawin
    Commented Oct 27, 2022 at 22:55
  • $\begingroup$ Or rather with $\ell$-adic Hodge theory... $\endgroup$
    – Piotr Achinger
    Commented Oct 28, 2022 at 9:52

0

Reset to default

You must log in to answer this question.

Browse other questions tagged .