5 papers
Modulus sheaves with transfers
Shane Kelly, Hiroyasu Miyazaki
We generalise Kahn, Miyazaki, Saito, Yamazaki's theory of modulus pairs to pairs consisting of a qcqs scheme equipped with an effective Cartier divisor representin…
Cdh descent, cdarc descent, and Milnor excision
Elden Elmanto, Marc Hoyois, Ryomei Iwasa +1
We give necessary and sufficient conditions for a cdh sheaf to satisfy Milnor excision, following ideas of Bhatt and Mathew. Along the way, we show that the cdh infinity-topos of a…
Smooth blowup square for motives with modulus
Shane Kelly, Shuji Saito
In this self-contained paper we prove that Voevodsky's smooth blowup triangle of motives generalises to a smooth blowup triangle of motives with modulus.
-theory of valuation rings
Shane Kelly, Matthew Morrow
We prove several results showing that the algebraic -theory of valuation rings behave as though such rings were regular Noetherian, in particular an analogue of the Geisser--Lev…
A better comparison of cdh- and ldh-cohomologies
Shane Kelly
In order to work with non-Nagata rings which are Nagata "up-to-completely-decomposed-universal-homeomorphism", specifically finite rank hensel valuation rings, we introduce the not…