Birational geometry and localisation of categories

Details Birational geometry and localisation of categories Birational geometry and localisation of categories

2008-05-24

arxiv.org/abs/0805.3753v1

Mathematics

Algebraic Geometry

69 pages

Scientific paper

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.

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