# The completely decomposed arc topology and motivic applications

Friday, August 13, 2021 12:00 PM

Elden Elmanto (Harvard)

I will introduce a Grothendieck topology, the cdarc topology, discovered in joint work with Marc Hoyois, Ryomei Iwasa and Shane Kelly which is a completely decomposed counterpart to Bhatt and Mathew's arc topology. It is a non-noetherian analog of Suslin-Voevodsky's cdh topology and is thus useful in the study of K-theory and algebraic cycles. I will focus on two applications to algebraic cycles and K-theory:

1) an excision result for algebraic cycles (joint with Hoyois, Iwasa and Kelly) and

2) a motivic refinement of the equivalence $L_{cdh}K = KH$ (joint with Matthew Morrow).