Birational geometry and localisation of categories

Bruno Kahn (1) , R. Sujatha (2)

1 IMJ - Institut de Mathématiques de Jussieu
2 School of Mathematics [TIFR]

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.

Mots clés: Localisation; birational geometry; places; R-equivalence

Domaines: Géométrie algébrique [math.AG]

Bruno Kahn, R. Sujatha. Birational geometry and localisation of categories. 2008. ⟨hal-00281764v1⟩