# The completely decomposed arc topology and motivic applications

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).

The synchronous discussion for Elden Elmanto’s talk is taking place not in zoom-chat, but at https://tinyurl.com/2021-08-13-ee (and will be deleted after ~3-7 days).