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Motivic exponential integrals and a motivic Thom-Sebastiani theorem. (English) Zbl 0966.14015

The authors give a motivic meaning of the Thom-Sebastiani theorem which states that the monodromy of the sum \(f(x)+g(y)\) of two germs of analytic functions is isomorphic to the product of the monodromies of each of the germs. This theorem relies on the product formula \(\int \exp(t(f\oplus g)) = \int \exp(t(f))\int \exp(t(g))\) for which the authors give a motivic integration analog. The theory of motivic integration was developed in earlier papers of the authors [J. Algebr. Geom. 7, 505-537 (1998; Zbl 0943.14010); Invent. Math. 135, 201-232 (1999; Zbl 0928.14004)].

MSC:

14F42 Motivic cohomology; motivic homotopy theory
32B10 Germs of analytic sets, local parametrization
32S35 Mixed Hodge theory of singular varieties (complex-analytic aspects)
14B05 Singularities in algebraic geometry
14G10 Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture)
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References:

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