2 research outputs found
On self-correspondences on curves
We study the algebraic dynamics of self-correspondences on a curve. A
self-correspondence on a (proper and smooth) curve over an algebraically
closed field is the data of another curve and two non-constant separable
morphisms and from to . A subset of is complete
if . We show that self-correspondences are divided
into two classes: those that have only finitely many finite complete sets, and
those for which is a union of finite complete sets. The latter ones are
called finitary and have a trivial dynamics. For a non-finitary
self-correspondence in characteristic zero, we give a sharp bound for the
number of \'etale finite complete sets.Comment: 34 pages, submitte