### Birational geometry and localisation of categories, by Bruno Kahn and R. Sujatha

We explore the relationships between the notions of places and rational
maps in birational geometry. In particular, over a field F of
characteristic 0, we show that in the category of smooth varieties
localised with respect to birational morphisms, the set of morphisms from
a variety X to a proper variety Y is the set of R-equivalence classes
Y(F(X))/R.

Bruno Kahn <kahn@math.jussieu.fr>

R. Sujatha <sujatha@math.tifr.res.in>