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中科院数学与系统科学研究院

数学研究所

 

数论研讨班

 

报告人Joseph AyoubUniversity of Zurich

 P^1-localisation and a possible definition of arithmetic Kodaira-Spencer classes

  2019.04.24(星期三),16:30-17:30

  点:晨兴楼110室(视频)

  要: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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