Integration in valued fields

  • Ehud Hrushovski
  • David Kazhdan
Part of the Progress in Mathematics book series (PM, volume 253)


We develop a theory of integration over valued fields of residue characteristic zero. In particular, we obtain new and base-field independent foundations for integration over local fields of large residue characteristic, extending results of Denef, Loeser, and Cluckers. The method depends on an analysis of definable sets up to definable bijections. We obtain a precise description of the Grothendieck semigroup of such sets in terms of related groups over the residue field and value group. This yields new invariants of all definable bijections, as well as invariants of measure-preserving bijections.


Open Ball Euler Characteristic Full Subcategory Closed Ball Grothendieck Group 
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Copyright information

© Birkhäuser Boston 2006

Authors and Affiliations

  • Ehud Hrushovski
    • 1
  • David Kazhdan
    • 1
  1. 1.Institute of MathematicsHebrew University of JerusalemJerusalemIsrael

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