9 citations · 48 across the 18 of their papers we have counts for
20 papers
Hypercomplete étale framed motives and comparison of stable homotopy groups of motivic spectra and étale realizations over a field
Andrei Druzhinin, Ola Sande
For any base field and integer invertible in , we prove that and commute with hyper étale sheafification …
Nisnevich equivalences of local essentially smooth open pairs
A. E. Druzhinin, A. A. Urzabaev
In this note, we prove a Nisnevich local equivalence \begin{equation*} X/(X-Z)\simeq X^\prime/(X^\prime-Z^\prime) \end{equation*} for essentially smooth local schemes and $X^\p…
Stable motivic trivial fibre decomposition over integers and framed motives
Andrei Druzhinin
Using the trivial fiber topology we describe motivic -loop spaces and fibrant replacements in the motivic stable homotopy category $\mathbf{SH}_{\mathbb{A}^1,\mathrm{Nis}}(…
Zariski-local framed -homotopy theory
Andrei Druzhinin, Vladimir Sosnilo
For any (not necessarily perfect) field we obtain equivalences of -categories \[\mathbf{H}^{\mathrm{fr},\mathrm{gp}}(k)\simeq \mathbf{H}^{\mathrm{fr},\mathrm{gp}}_{\mat…
Strict homotopy invariance via compactified homotopies and correspondences, and fibres of essentially smooth schemes over one-dimensional base schemes
Andrei Druzhinin
We develop the technique of compactified correspondences and homotopies over one-dimensional base schemes, and illuminate the perfectness and the inverting of characteristic assump…
The trivial fiber topology and framed motives over the integers
A. Druzhinin, Håkon Kolderup, Paul Arne Østvær
This paper introduces the trivial fiber topology on schemes. For one-dimensional base schemes, we use it to describe fibrant replacements in the stable motivic homotopy category an…
Stable connectivity over a base
A. Druzhinin
Morel's stable connectivity theorems state that for any connective -spectrum of motivic spaces (Nisnevich simplicial sheaves) over an arbitrary field, the spectrum $L_{\ma…
Geometric models for fibrant resolutions of motivic suspension spectra
Andrei Druzhinin
We construct geometric models for the -spectrum , which computes in Garkusha-Panin's theory of framed motives \cite{GP14} a positively motivically…
Rigidity for smooth affine pairs over a field
A. Druzhinin
Let be a closed immersion of smooth affine schemes over an arbitrary field , and denote the henselization of along . For each presheaf $E\colon \mathbf{S…
Framed correspondences and the zeroth stable motivic homotopy group in odd characteristic
Andrei Druzhinin, Jonas Irgens Kylling
We extend the results of G.~Garkusha and I.~Panin on framed motives of algebraic varieties [4] to the case of a finite base field, and extend the computation of the zeroth cohomolo…
The homomorphism of presheaves over a base
A. Druzhinin
We construct the homomorphism of presheaves over an arbitrary base scheme , where is the (naive) Milnor-Witt K-…
Surjectivity of the etale excision map for homotopy invariant framed presheaves
Andrei Druzhinin, Ivan Panin
The category of framed correspondences Fr_*(k), framed presheaves and framed sheaves were invented by Voevodsky in his unpublished notes [17]. Based on the notes [17] a new approac…
Cohomological correspondence categories
Andrei Druzhinin, Håkon Kolderup
We prove that homotopy invariance and cancellation properties are satisfied by any linear category of correspondences that is defined, via Calmès and Fasel's construction, by an un…
Framed motives of smooth affine pairs
A. E. Druzhinin
The theory of framed motives by Garkusha and Panin gives computations in the stable motivic homotopy category in terms of Voevodsky's framed correspondences. In pa…
Cancellation theorem for Grothendieck-Witt-correspondences and Witt-correspondences
Andrei Druzhinin
The cancellation theorem for Grothendieck-Witt-correspondences and Witt-correspondences between smooth varieties over an infinite prefect field , , is proved, the…
Effective Grothendieck-Witt motives of smooth varieties
Andrei Druzhinin
The category of effective Grothendieck-Witt-motives (and Witt-motives ) by Voevodsky-Suslin method startin…
Strictly homotopy invariance of Nisnevich sheaves with GW-transfers
Andrei Druzhinin
The strictly homotopy invariance of the associated Nisnevish sheave of a homotopy invariant presheave with GW-transfers (or Witt-transfe…
Rigidity theorem for presheaves with Witt-transfers
Andrei Druzhinin
The rigidity theorem for homotopy invariant presheaves with Witt-transfers on the category of smooth affine varieties over a field with characteristic not equal to 2 is proved.…
Rigidity for linear framed presheaves and generalized motivic cohomology theories
Alexey Ananyevskiy, Andrei Druzhinin
A rigidity property for the homotopy invariant stable linear framed presheaves is established. As a consequence a variant of Gabber rigidity theorem is obtained for a cohomology th…
Triangulated category of effective -motives
Andrei Druzhinin
The category of effective -motives with functor defining motives of smooth affine varieties for perfect field , is co…