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Nearby motivic sheaves of weighted equivariant functions

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KAH2 - K-theory, algebraic cycles and motivic homotopy theory

Let X be a smooth algebraic variety (over a field of characteristic zero) endowed with a multiplicative action of the affine line. In a recent work with Julien Sebag we show that the nearby motivic sheaf functor of a weighted equivariant function on X commutes with direct images and proper direct images. In this talk, I will sketch the proof of this result and provide some motivation. In particular I will explain how our result provides a generalized functorial version within the stable homotopy category of schemes of conjectures by Behrend-Bryan-Szendrői and Davison-Meinhardt originally formulated as an equality between virtual motives.

This talk is part of the Isaac Newton Institute Seminar Series series.

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