The modified diagonal cycle on the triple product of a pointed curve
Publication
, Journal Article
Gross, BH; Schoen, C
Published in: Annales de l'Institut Fourier
Let
be a curve over a field
with a rational point
. We define a canonical cycle
. Suppose that
is a number field and that
has semi-stable reduction over the integers of
with fiber components non-singular. We construct a regular model of
and show that the height pairing
is well defined where
and
are correspondences. The paper ends with a brief discussion of heights and
-functions in the case that
is a modular curve.
