Jean-Benoit Bost (Paris-Sud):
"A-analytic curves in algebraic varieties over number fields and Arakelov positivity"

Abstract:

This talk will be devoted to some recent joint work with A. Chambert-Loir (Rennes).

Let $X$ be a variety over a number field $K$, and let $\varphi:
{\rm Spf} K[[T]] \rightarrow X$ be a formal curve which is
$K_v$-analytic for all
places $v$ of $K$. This talk will discuss various geometric conditions on the
``size" of  $\varphi$ at various places $v$ which would imply either the rationality, or  the algebraicity of $\varphi$.

The  case where
$\varphi$ is an integral curve of an algebraic differential equation
will be particularly considered.