Motivic integration on smooth rigid varieties and invariants of degenerations
By François Loeser, Julien Sebag. 2001
91 citations recorded by the source corpus.
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.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/100b7a5358a1717efd60bbfbe6c2a143110fc245
How researchers see this paper
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In Geometry and Topology
- L. H. Halle
- Leonard Lipshitz
- Raf Cluckers
- David Kazhdan
- Ehud Hrushovski
- Johannes Nicaise
- M. Temkin
- François Loeser
In Mathematical Physics
- L. H. Halle
- Leonard Lipshitz
- David Kazhdan
- Johannes Nicaise
- Ehud Hrushovski
- Raf Cluckers
- M. Temkin
- François Loeser
Citations in the corpus
- A trace formula for rigid varieties, and motivic Weil generating series for formal schemes (2007, methodology): “The theory of motivic integration on stft formal R-schemes was developed in [35], and this theory was used to define motivic integrals of differential forms of maximal degree on smooth quasi-compact rigid varieties in [29].”
- Analytic cell decomposition and analytic motivic integration (2005, background): “Another approach to analytic motivic integration, based on entire models of rigid varieties and the theory of Néron models instead of cell decomposition, is developed by Sebag and Loeser in [35], and by Sebag in [42].”
- Integration in valued fields (2005, result): “the Grothendieck ring K(VarF) of algebraic varieties over F; and another in K(VarF)[[A1]−1] ( Proposition 10.8). It is instructive to compare this with the INTEGRATION IN VALUED FIELDS 7 invariant of [24], with values in K(RES[n])/[Gm]. 1 Since any two closed balls are isomorphic, via additive trans”
- Motivic zeta functions of abelian varieties, and the monodromy conjecture (2009, methodology): “By [22, 4.3.1], the right-hand side of (2.1) equals U η i ω | .”