55 citations · 257 across the 22 of their papers we have counts for
24 papers
Descendability and descent in topological weaves
Adeel A. Khan
We prove a criterion for a finitely presented surjection of algebraic spaces to be descendable in a topological weave. We apply this to show that étale motivic spectra satisfy -…
Cohomological and categorical concentration
Adeel A. Khan, Charanya Ravi
Given a torus action on a compact space X, a fundamental result of Borel and Atiyah-Segal asserts that the equivariant cohomology of X is concentrated in the fixed locus X^T, up to…
The lattice property for perfect complexes on singular stacks
Adeel A. Khan
Let C be the stable oo-category of perfect complexes on a derived Deligne-Mumford stack X of finite type over the complex numbers. We prove that the complexified noncommutative top…
Equivariant generalized cohomology via stacks
Adeel A. Khan, Charanya Ravi
We prove a general form of the statement that the cohomology of a quotient stack can be computed by the Borel construction. It also applies to the lisse extensions of generalized c…
Virtual localization revisited
Dhyan Aranha, Adeel A. Khan, Alexei Latyntsev +2
Let be a split torus acting on an algebraic scheme with fixed locus . Edidin and Graham showed that on localized -equivariant Chow groups, (a) push-forward alon…
Absolute Poincaré duality in étale cohomology
Adeel A. Khan
We extend Poincaré duality in étale cohomology from smooth schemes to regular ones. This is achieved via a formalism of trace maps for local complete intersection morphisms.
Generalized cohomology theories for algebraic stacks
Adeel A. Khan, Charanya Ravi
We extend the stable motivic homotopy category of Voevodsky to the class of scalloped algebraic stacks, and show that it admits the formalism of Grothendieck's six operations. Obje…
K-theory and G-theory of derived algebraic stacks
Adeel A. Khan
These are some notes on the basic properties of algebraic K-theory and G-theory of derived algebraic spaces and stacks, and the theory of fundamental classes in this setting.
Categorical Milnor squares and K-theory of algebraic stacks
Tom Bachmann, Adeel A. Khan, Charanya Ravi +1
We introduce a notion of Milnor square of stable -categories and prove a criterion under which algebraic K-theory sends such a square to a cartesian square of spectra. We a…
On the rational motivic homotopy category
Frédéric Déglise, Jean Fasel, Adeel A. Khan +1
We study the structure of the rational motivic stable homotopy category over general base schemes. Our first class of results concerns the six operations: we prove absolute purity,…
On the infinite loop spaces of algebraic cobordism and the motivic sphere
Tom Bachmann, Elden Elmanto, Marc Hoyois +3
We obtain geometric models for the infinite loop spaces of the motivic spectra , , and over a field. They are motivically equivalent to $\m…
Virtual fundamental classes of derived stacks I
Adeel A. Khan
We construct the étale motivic Borel-Moore homology of derived Artin stacks. Using a derived version of the intrinsic normal cone, we construct fundamental classes of quasi-smooth…
Virtual excess intersection theory
Adeel A. Khan
We prove a K-theoretic excess intersection formula for derived Artin stacks. When restricted to classical schemes, it gives a refinement and new proof of R. Thomason's formula.
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…
Borel isomorphism and absolute purity
Frédéric Déglise, Jean Fasel, Fangzhou Jin +1
We prove absolute purity for the rational motivic sphere spectrum. The main ingredient is the construction of an analogue of the Chern character, where algebraic K-theory is replac…
Regularity of spectral stacks and discreteness of weight-hearts
Vladimir Sosnilo
We study regularity in the context of ring spectra and spectral stacks. Parallel to that, we construct a weight structure on the category of compact quasi-coherent sheaves on spect…
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…
Algebraic K-theory of quasi-smooth blow-ups and cdh descent
Adeel A. Khan
We construct a semi-orthogonal decomposition on the category of perfect complexes on the blow-up of a derived Artin stack in a quasi-smooth centre. This gives a generalization of T…
Framed transfers and motivic fundamental classes
Elden Elmanto, Marc Hoyois, Adeel A. Khan +2
We relate the recognition principle for infinite -loop spaces to the theory of motivic fundamental classes of Déglise, Jin, and Khan. We first compare two kinds of tra…
Fundamental classes in motivic homotopy theory
Frédéric Déglise, Fangzhou Jin, Adeel A. Khan
We develop the theory of fundamental classes in the setting of motivic homotopy theory. Using this we construct, for any motivic spectrum, an associated bivariant theory in the sen…
Virtual Cartier divisors and blow-ups
Adeel A. Khan, David Rydh
We prove a universal property for blow-ups in regularly immersed subschemes, based on a notion we call "virtual effective Cartier divisor". We also construct blow-ups of quasi-smoo…
Motivic infinite loop spaces
Elden Elmanto, Marc Hoyois, Adeel A. Khan +2
We prove a recognition principle for motivic infinite P1-loop spaces over a perfect field. This is achieved by developing a theory of framed motivic spaces, which is a motivic anal…
A^1-homotopy invariance in spectral algebraic geometry
Denis-Charles Cisinski, Adeel A. Khan
We study two different flavours of A^1-homotopy theory in the setting of spectral algebraic geometry, and compare them to classical A^1-homotopy theory. As an application we show t…
The Morel-Voevodsky localization theorem in spectral algebraic geometry
Adeel A. Khan
We prove an analogue of the Morel-Voevodsky localization theorem over spectral algebraic spaces. As a corollary we deduce a "derived nilpotent invariance" result which, informally…