Germs of paths on algebraic varieties: a gentle introduction to motivic integration
François Loeser, Ecole Normale Supérieure, Paris, France
Abstract
Roughly speaking motivic integration is
a geometric integration theory on the space of infinitesimal
paths on an algebraic variety.
Some of the main applications of motivic integration will be discussed,
including applications to
birational geometry, monodromy and the Ax-Kochen principle,
with a special emphasis to geometric aspects.