| Abstract: |
According to Beilinson’s philosophy, there should be a descending multiplicative filtration, called a motivic filtration, on the K-theory functor K on qcqs schemes. When K is restricted to smooth schemes over a perfect field, such a filtration has been satisfactorily constructed by Bloch-Lichtenbaum, Friedlander-Suslin, Levine, Voevodsky and Grayson. I will begin my talk with some background on motivic filtration of K-theory and will explain Levine’s construction, which is known as homotopy coniveau tower. Then I will explain my joint work with Wataru Kai and Amalendu Krishna to extend this construction to possibly singular (possibly reduced) schemes by using algebraic cycles with modulus. |
