Motivic Integration on Smooth Rigid Varieties and Invariants of Degenerations

@inproceedings{Loeser2003MotivicIO,
  title={Motivic Integration on Smooth Rigid Varieties and Invariants of Degenerations},
  author={François Loeser and Julien A Sebag},
  year={2003}
}
We develop a theory of motivic integration for smooth rigid varieties. As an application we obtain a motivic analogue for rigid varieties of Serre’s invariant for p-adic varieties. Our construction provides new geometric birational invariants of degenerations of algebraic varieties. For degenerations of Calabi-Yau varieties, our results take a stronger form.