Motivic Exponential Integrals and a Motivic Thom-sebastiani Theorem
نویسنده
چکیده
1.1. Let f and f ′ be germs of analytic functions on smooth complex analytic varieties X and X ′ and consider the function f ⊕ f ′ on X × X ′ given by f ⊕ f (x, x) = f(x) + f (x). The Thom-Sebastiani Theorem classically states that the monodromy of f ⊕ f ′ on the nearby cycles is isomorphic to the product of the monodromy of f and the monodromy of f ′ (in the original form of the Theorem [18] the functions were assumed to have isolated singularities). It is now a common idea that the Thom-Sebastiani Theorem is best understood by using Fourier transformation and exponential integrals because of the formula ∫ exp(t(f ⊕ f )) = ∫ exp(tf) · ∫ exp(tf ). (1.1)
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تاریخ انتشار 1999