12 citations · 48 across the 15 of their papers we have counts for
18 papers
Some explicit counter-examples to Weibel's conjecture
Shane Kelly
We give two related but different methods for constructing rings of Krull dimension 1 and . The first works for , and the second works for any $d \geq…
Hodge cohomology with a ramification filtration, II
Shane Kelly, Hiroyasu Miyazaki
As a sequel of Part I, we consider a filtration of Hodge cohomology groups indexed by divisors "at infinity", and prove that they are represented in the category of motives with mo…
Hodge cohomology with a ramification filtration, I
Shane Kelly, Hiroyasu Miyazaki
We consider a filtration on the cohomology of the structure sheaf indexed by (not necessarily reduced) divisors ``at infinity''. We show that the filtered pieces have transfers mor…
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…
Milnor excision for motivic spectra
Elden Elmanto, Marc Hoyois, Ryomei Iwasa +1
We prove that the -category of motivic spectra satisfies Milnor excision: if is a morphism of commutative rings sending an ideal isomorphically onto a…
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…
Differential forms in positive characteristic II: cdh-descent via functorial Riemann-Zariski spaces
Annette Huber, Shane Kelly
This paper continues our study of the sheaf associated to Kähler differentials in the cdh-topology and its cousins, in positive characteristic, without assuming resolution of singu…
Mixed Motives and Geometric Representation Theory in Equal Characteristic
Jens Niklas Eberhardt, Shane Kelly
Let be a field of characteristic . We introduce a formalism of mixed sheaves with coefficients in and showcase its use in representation theory. More p…
Some observations about motivic tensor triangulated geometry over a finite field
Shane Kelly
We give a brief introduction to tensor triangulated geometry, a brief introduction to various motivic categories, and then make some observations about the conjectural structure of…
Weight homology of motives
Shane Kelly, Shuji Saito
In the first half of this article we define a new weight homology functor on Voevodsky's category of effective motives, and investigate some of its properties. In special cases we…
Differential forms in positive characteristic avoiding resolution of singularities
Annette Huber, Stefan Kebekus, Shane Kelly
This paper studies several notions of sheaves of differential forms that are better behaved on singular varieties than Kähler differentials. Our main focus lies on varieties that a…
Points in algebraic geometry
Ofer Gabber, Shane Kelly
We give scheme-theoretic descriptions of the category of fibre functors on the categories of sheaves associated to the Zariski, Nisnevich, étale, rh, cdh, ldh, eh, qfh, and h topol…
The motivic Steenrod algebra in positive characteristic
Marc Hoyois, Shane Kelly, Paul Arne Østvær
Let S be an essentially smooth scheme over a field and l a prime number invertible on S. We show that the algebra of bistable operations in the mod l motivic cohomology of smooth S…
Triangulated categories of motives in positive characteristic
Shane Kelly
This thesis presents a way to apply this theorem of Gabber to a large portion of Voevodsky's work in order to lift the assumption that resolution of singularities holds. This gives…
Vanishing of negative -theory in positive characteristic
Shane Kelly
We show how a theorem of Gabber on alterations can be used to apply work of Cisinski, Suslin, Voevodsky, and Weibel to prove that for where is…