Modul: MAT770 Oberseminar: Algebraische Geometrie

## On motivic cohomology of singular algebraic schemes

Talk by Dr. Jinhyun Park

**Date:** 13.12.21 **Time:** 13.15 - 15.00 **Room:**

On the category of smooth schemes over a field, it is known that the motivic cohomology is described by the higher Chow groups of S. Bloch. Although the higher Chow groups are defined for singular schemes as well, they do not behave well on singular ones, so that no longer do they provide the right candidates for the motivic cohomology on the larger category of all algebraic schemes. In this talk, I sketch some recent attempts of mine to provide a new algebraic-cycle-based functorial candidate for the motivic cohomology on the category of algebraic schemes. This new candidate coincides with the higher Chow theory on smooth schemes, detects nilpotence, and satisfies a few nice properties. This approach is done via formal geometry and some ideas from derived algebraic geometry. As this is very complicated, as an illustration I give an example on the concrete case of the fat points, where the situation is simpler, but still not trivial.

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