科研之友
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摘要
We prove that the construction of motivic nearby cycles, introduced by Jan Denef and Fran double dagger ois Loeser, is compatible with the formalism of nearby motives, developed by Joseph Ayoub. Let be an arbitrary field of characteristic zero, and let be a smooth quasi-projective -scheme. Precisely, we show that, in the Grothendieck group of constructible ,tale motives, the image of the nearby motive associated with a flat morphism of -schemes , in the sense of Ayoub's theory, can be identified with the image of Denef and Loeser's motivic nearby cycles associated with . In particular, it provides a realization of the motivic Milnor fiber of in the "non-virtual" motivic world.
- 出版日期2013-11
