Motivic integration

Motivic integrationis a notion inalgebraic geometrythat was introduced byMaxim Kontsevichin 1995 and was developed byJan DenefandFrançois Loeser.Since its introduction it has proved to be quite useful in various branches ofalgebraic geometry,most notablybirational geometryandsingularity theory.Roughly speaking, motivic integration assigns to subsets of the arc space of an algebraic variety, a volume living in theGrothendieck ringofalgebraic varieties.The naming 'motivic' mirrors the fact that unlike ordinaryintegration,for which the values arereal numbers,in motivic integration the values are geometric in nature.

External links

• AMS Bulletin Vol. 42Tom Hales
  • What is motivic measure?
• Lecture Notes (2019)Devlin Mallory
  • Motivic Integration
• math.AG/9911179A.Craw
  • An introduction tomotivic integration
• Lecture Notes (version of 2008)François Loeser
  • Seattle lecture notes on motivic integration
• Lecture NotesW.Veys
  • Arc spaces, motivic integration and stringy invariants