Lecture----数学院晨兴数学中心

Title:	P^1-localisation and a possible definition of arithmetic Kodaira-Spencer classes
Speaker:	Joseph Ayoub (University of Zurich)
Time:	2019-4-24, 16:30-17:30
Place:	MCM;110
Abstract:	A^1-localisation is a universal construction which produces “cohomology theories" for which the affine line A^1 is contractible. It plays a central role in the theory of motives à la Morel-Voevodsky. In this talk, I'll discuss the analogous construction where the affine line is replaced by the projective line P^1. This is the P^1-localisation which is arguably an unnatural construction since it produces "cohomology theories" for which the projective line P^1 is contractible. Nevertheless, I'll explain a few positive results and some computations around this construction which naturally lead to a definition of Kodaira-Spencer classes of arithmetic nature. (Unfortunately, it is yet unclear if these classes are really interesting and nontrivial.)
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