8 papers · 1 filter
-connected components of classifying spaces and purity for torsors
Elden Elmanto, Girish Kulkarni, Matthias Wendt
In this paper, we study the Nisnevich sheafification of the presheaf associating to a smooth scheme the set of isomorphism classes of -torsors, f…
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…
Scheiderer motives and equivariant higher topos theory
Elden Elmanto, Jay Shah
We give an algebro-geometric interpretation of -equivariant stable homotopy theory by means of the -topology introduced by Claus Scheiderer in his study of -torsion phen…
Descent for semiorthogonal decompositions
Benjamin Antieau, Elden Elmanto
We prove descent theorems for semiorthogonal decompositions using techniques from derived algebraic geometry. Our methods allow us to capture more general filtrations of derived ca…
Modules over algebraic cobordism
Elden Elmanto, Marc Hoyois, Adeel A. Khan +2
We prove that the -category of -modules over any scheme is equivalent to the -category of motivic spectra with finite syntomic transfers. Using the re…
Perfection in motivic homotopy theory
Elden Elmanto, Adeel A. Khan
We prove a topological invariance statement for the Morel-Voevodsky motivic homotopy category, up to inverting exponential characteristics of residue fields. This implies in partic…