Ivan Panin 2/3 - A Local Construction of Stable Motivic Homotopy Theory

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Описание видео: Notes: nextcloud.ihes.fr/index.php/s/dDbMXEc36JQyKts V. For the first two applications I choose k = ℂ for simplicity. I will also discuss several applications. Voevodsky [6] invented the category of framed correspondences with the hope to give a new construction of stable motivic homotopy theory SH(k) which will be more friendly for computational purposes. Let Fr(Y,X) be the pointed set of stable framed correspondences between smooth algebraic varieties Y and X. Joint with G. Garkusha we used framed correspondences to develop the theory of framed motives in [4]. In my lectures I will recall the definition of framed correspondences and describe the genuinely local model for SH(k) (assuming that the base field k is infinite and perfect). (1) The simplicial space Fr(... In particular, we get rid of motivic equivalences completely. For further two applications k is any infinite and perfect field. This theory led us in [5] to a genuinely local construction of SH(k).

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