# The completely decomposed arc topology and motivic applications

### Elden Elmanto (Harvard)

13-Aug-2021, 19:00-20:00 (20 months ago)

Abstract: 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 Tom Bachmann and Matthew Morrow).

algebraic geometry

Audience: researchers in the topic

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

Series comments: The seminar is sometimes online, and sometimes in person.

For zoom talks: This seminar requires both advance registration, and a password. Register at stanford.zoom.us/meeting/register/tJEvcOuprz8vHtbL2_TTgZzr-_UhGvnr1EGv Password: 362880

If you have registered once, you are always registered for the seminar, and can join any future talk using the link you receive by email. If you lose the link, feel free to reregister. This might work too: stanford.zoom.us/j/95272114542

More seminar information (including slides and videos, when available): agstanford.com

 Organizer: Ravi Vakil* *contact for this listing

Export talk to