Schemic Grothendieck Rings Ii: Jet Schemes and Motivic Integration
نویسنده
چکیده
We generalize the notion of a jet scheme (truncated arc space) to arbitrary fat points via adjunction, and show that this yields for each fat point, an endomorphism on each schemic Grothendieck ring as defined in [17]. We prove that some of the analogues for linear jets still hold true, like locally trivial fibration over the smooth locus. In this formalism, we can define several generating zeta series, motivic series, the rationality of which can now be investigated. We use the theory of jet schemes to define a local motivic integration with values in the formal Grothendieck ring.
منابع مشابه
Schemic Grothendieck Rings and Motivic Rationality
We propose a suitable substitute for the classical Grothendieck ring of an algebraically closed field, in which any quasi-projective scheme is represented, while maintaining its non-reduced structure. This yields a more subtle invariant, called the schemic Grothendieck ring, in which we can formulate a form of integration resembling Kontsevich’s motivic integration via arc schemes. In view of i...
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