18 citations · 53 across the 11 of their papers we have counts for
18 papers
Semiorthogonal decompositions for families of twisted flag varieties
Alexey Ananyevskiy, Alexander Samokhin
We show that the derived categories of smooth families of twisted generalized flag varieties admit semiorthogonal decompositions into derived categories of twisted sheaves over the…
Chow rings of quasi-split geometrically almost simple algebraic groups
Alexey Ananyevskiy, Nikita Geldhauser
We compute the Chow ring of a quasi-split geometrically almost simple algebraic group assuming the coefficients to be a field. This extends the classical computation for split grou…
Combing a hedgehog over a field
Alexey Ananyevskiy, Marc Levine
We investigate the question of the existence of a non-vanishing section of the tangent bundle on a smooth affine quadric hypersurface over a given perfect field . In case…
The motivic Adams conjecture
Alexey Ananyevskiy, Elden Elmanto, Oliver Röndigs +1
We solve a motivic version of the Adams conjecture with the exponential characteristic of the base field inverted. In the way of the proof we obtain a motivic version of mod k Dold…
On the -Euler characteristic of the variety of maximal tori in a reductive group
Alexey Ananyevskiy
We show that for a reductive group over a field the -Euler characteristic of the variety of maximal tori in is an invertible element of the Grothendieck-W…
Thom isomorphisms in triangulated motivic categories
Alexey Ananyevskiy
We show that a triangulated motivic category admits categorical Thom isomorphisms for vector bundles with an additional structure if and only if the generalized motivic cohomology…
SL-oriented cohomology theories
Alexey Ananyevskiy
We show that a representable motivic cohomology theory admits a unique normalized SL^c-orientation if the zeroth cohomology presheaf is a Zariski sheaf. We also construct Thom isom…
On very effective hermitian -theory
Alexey Ananyevskiy, Oliver Röndigs, Paul Arne Østvær
We argue that the very effective cover of hermitian -theory in the sense of motivic homotopy theory is a convenient algebro-geometric generalization of the connective real topol…
Framed and MW-transfers for homotopy modules
Alexey Ananyevskiy, Alexander Neshitov
In the paper we use the theory of framed correpondences to construct Milnor-Witt transfers on homotopy modules. As a consequence we identify the zeroth stable -homoto…
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…
On the zeroth stable -homotopy group of a smooth curve
Alexey Ananyevskiy
We provide a cohomological interpretation of the zeroth stable -homotopy group of a smooth curve over an infinite perfect field. We show that this group is isomorphic…
Cancellation theorem for framed motives of algebraic varieties
Alexey Ananyevskiy, Grigory Garkusha, Ivan Panin
The machinery of framed (pre)sheaves was developed by Voevodsky [V1]. Based on the theory, framed motives of algebraic varieties are introduced and studied in [GP1]. An analog of V…
Witt sheaves and the -inverted sphere spectrum
Alexey Ananyevskiy, Marc Levine, Ivan Panin
Ananyevsky has recently computed the stable operations and cooperations of rational Witt theory. These computations enable us to show a motivic analog of Serre's finiteness result:…
Stable operations and cooperations in derived Witt theory with rational coefficients
Alexey Ananyevskiy
The algebras of stable operations and cooperations in derived Witt theory with rational coefficients are computed and an additive description of cooperations in derived Witt theory…
On the push-forwards for motivic cohomology theories with invertible stable Hopf element
Alexey Ananyevskiy
We present a geometric construction of push-forward maps along projective morphisms for cohomology theories representable in the stable motivic homotopy category assuming that the…
On the relation of special linear algebraic cobordism to Witt groups
Alexey Ananyevskiy
We reconstruct derived Witt groups via special linear algebraic cobordism. There is a morphism of ring cohomology theories which sends the canonical Thom class in special linear co…
Exceptional collections of line bundles on projective homogeneous varieties
Alexey Ananyevskiy, Asher Auel, Skip Garibaldi +1
We construct new examples of exceptional collections of line bundles on the variety of Borel subgroups of a split semisimple linear algebraic group G of rank 2 over a field. We exh…
The special linear version of the projective bundle theorem
Alexey Ananyevskiy
A special linear Grassmann variety SGr(k,n) is the complement to the zero section of the determinant of the tautological vector bundle over Gr(k,n). For a representable ring cohomo…