7 papers
The Lichtenbaum-Quillen dimension of complex varieties
Nicolas Addington, Elden Elmanto
The Lichtenbaum-Quillen conjecture for smooth complex varieties states that algebraic and topological K-theory with finite coefficients become isomorphic in high degrees. We define…
Motivic cohomology of equicharacteristic schemes
Elden Elmanto, Matthew Morrow
We construct a theory of motivic cohomology for quasi-compact, quasi-separated schemes of equal characteristic, which is related to non-connective algebraic -theory via an Atiya…
Motivic Steenrod operations at the characteristic via infinite ramification
Toni Annala, Elden Elmanto
We construct motivic power operations on the mod- motivic cohomology of $\Fb_p$-schemes using a motivic refinement of NizioÅ's theorem. The key input is a purity theorem for mo…
-invariant motivic cohomology of schemes
Tom Bachmann, Elden Elmanto, Matthew Morrow
Voevodsky outlined a conjectural programme that his slice filtration in motivic homotopy theory should give rise to a good theory of -invariant motivic cohomology. Th…
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 filtered algebraic -theory of stacks I: characteristic zero
Elden Elmanto, Dmitry Kubrak, Vladimir Sosnilo
Given a compact Lie group acting on a space , the classical Atiyah-Segal completion theorem identifies topological -theory of the homotopy quotient with an explicit…