Seminar on Arithmetic Geometry

Clémentine Lemarié—Rieusset (University of Burgundy)

In this talk I will present motivic linking, a new application in algebraic geometry of motivic homotopy theory (specifically, of quadratic intersection theory). Over a perfect field F, motivic linking consists in the study of how two (nice) closed F-subschemes of a (nice) ambient F-scheme are linked (i.e. intertwined) and is a counterpart to linking in knot theory. More specifically, I will present counterparts in algebraic geometry to the linking number of two oriented disjoint knots (the number of times one of the knots turns around the other knot). For the most part, these counterparts take values in the Witt group of F or in the Grothendieck-Witt group of F, rather than in the group of integers. There will be several examples, including closed immersions between smooth models of motivic spheres and closed immersions between projective spaces.

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