Abstract: |
Grothendieck predicted the existence of a universal cohomology theory, called motives, which unifies various cohomologies in arithmetic geometry. The theory of motives à la Voevodsky partially realises this idea, but his theory does not capture some important arithmetic phenomena such as wild ramifications. In this talk, after recalling Voevodsky’s theory briefly, I will explain the recent development of the theory of motives with modulus: a generalisation of Voevodsky’s motives which captures more arithmetic information. This is a joint work with Bruno Kahn, Shuji Saito and Takao Yamazaki. |