Gross--Schoen Cycles and Dualising Sheaves

Details Gross--Schoen Cycles and Dualising Sheaves Gross--Schoen Cycles and Dualising Sheaves

2008-12-01

arxiv.org/abs/0812.0371v1

Mathematics

Number Theory

Scientific paper

The aim of this paper is to study the modified diagonal cycle in the triple
product of a curve over a global field defined by Gross and Schoen. Our main
result is an identity between the height of this cycle and the
self-intersection of the relative dualising sheaf. We have some applications to
the following problems in number theory and algebraic geometry.

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