28 citations · 66 across the 16 of their papers we have counts for
19 papers
Cartier crystals and dual-constructible -torsion complexes
Jefferson Baudin, Kay Rülling
We show that given a Noetherian and -finite scheme, the fixed point functor on Cartier crystals is fully faithful to the category of sheaves on the flat and relatively perfect s…
Lectures on the cohomology of reciprocity sheaves
Nikolai Opdan, Kay Rülling
These are the notes accompanying three lectures given by the second author at the Motivic Geometry program at CAS, which aim to give an introduction and an overview of some recent…
Ramification theory of reciprocity sheaves, II, Higher local symbols
Kay Rülling, Shuji Saito
We construct a theory of higher local symbols along Parsin chains for reciprocity sheaves. Applying this formalism to differential forms, gives a new construction of the Parsin-Lom…
Ramification theory of reciprocity sheaves, I, Zariski-Nagata purity
Kay Rülling, Shuji Saito
We prove a Zariski-Nagata purity theorem for the motivic ramification filtration of a reciprocity sheaf. An important tool in the proof is a generalization of the Kato-Saito recipr…
Cycle class maps for Chow groups of zero-cycles with modulus
Kay Rülling, Shuji Saito
For a quasi-projective smooth scheme X of pure dimension d over a field k and an effective Cartier divisor D on X whose support is a simple normal crossing divisor, we construct a…
Loops on schemes and the algebraic fundamental group
Kay Rülling, Stefan Schröer
In this note we give a re-interpretation of the algebraic fundamental group for proper schemes that is rather close to the original definition of the fundamental group for topologi…
On the cohomology of reciprocity sheaves
Federico Binda, Kay Rülling, Shuji Saito
In this paper we show the existence of an action of Chow correspondences on the cohomology of reciprocity sheaves. In order to do so, we prove a number of structural results, such…
Tensor structures in the theory of modulus presheaves with transfers
Kay Rülling, Rin Sugiyama, Takao Yamazaki
The tensor product of -invariant sheaves with transfers introduced by Voevodsky is generalized to reciprocity sheaves via the theory of modulus presheaves with transf…
Reciprocity sheaves and their ramification filtrations
Kay Rülling, Shuji Saito
We define a motivic conductor for any presheaf with transfers using the categorical framework developed for the theory of motives with modulus by Kahn-Miyazaki-Saito-Yamazaki.…
Suslin homology of relative curves with modulus
Kay Rülling, Takao Yamazaki
We compute the Suslin homology of relative curves with modulus. This result may be regarded as a modulus version of the computation of motives for curves, due to Suslin and Voevods…
Higher Chow groups with modulus and relative Milnor K-theory
Kay Rülling, Shuji Saito
Let X be a smooth variety over a field k and D an effective divisor whose support has simple normal crossings. We construct an explicit cycle map from the r-th Nisnevich motivic co…
Introductory course on -adic sheaves and their ramification theory on curves
Lars Kindler, Kay Rülling
These are the notes accompanying 13 lectures given by the authors at the Clay Mathematics Institute Summer School 2014 in Madrid. The notes give an introduction into the theory of…
Vanishing of the higher direct images of the structure sheaf
Andre Chatzistamatiou, Kay Rülling
We prove that the higher direct images of the structure sheaf under a birational and projective morphism between excellent and regular schemes vanish.
Reciprocity sheaves
Bruno Kahn, Shuji Saito, Takao Yamazaki
We start developing a notion of reciprocity sheaves, generalizing Voevodsky's homotopy invariant presheaves with transfers which were used in the construction of his triangulated c…
K-Groups of reciprocity functors for G_a and abelian varieties
Kay Rülling, Takao Yamazaki
We prove that the -group of reciprocity functors, defined by F. Ivorra and the first author, vanishes over a perfect field as soon as one of the reciprocity functors is $\mathbb…
K-groups of reciprocity functors
Florian Ivorra, Kay Rülling
In this work we introduce reciprocity functors, construct the associated K-group of a family of reciprocity functors, which itself is a reciprocity functor, and compute it in sever…
Rational points over finite fields for regular models of algebraic varieties of Hodge type
Pierre Berthelot, Hélène Esnault, Kay Rülling
Let be a discrete valuation ring of mixed characteristics , with finite residue field and fraction field , let be a finite extension of , and let be a…
Higher direct images of the structure sheaf in positive characteristic
Andre Chatzistamatiou, Kay Rülling
We prove vanishing of the higher direct images of the structure (and the canonical) sheaf for a proper birational morphism with source a smooth variety and target the quotient of a…
Characteristic 0 and p analogies, and some motivic cohomology
Manuel Blickle, Hélène Esnault, Kay Rülling
The purpose of this survey is to explain some recent results about analogies between characteristic 0 and characteristic geometry, and to discuss an infinitesimal variant of…