8 papers
Deformation to the normal bundle and blow-ups via derived Weil restrictions
Jeroen Hekking, Adeel A. Khan, David Rydh
We develop an analogue of the deformation to the normal cone in the context of derived algebraic geometry. This provides any given morphism of derived stacks with a degeneration to…
Period sheaves via perverse pullbacks
Adeel A. Khan, Tasuki Kinjo, Hyeonjun Park +1
We construct period sheaves for Hamiltonian spaces, as conjectured in the work of Ben-Zvi, Sakellaridis and Venkatesh, using the perverse pullback functors introduced in the author…
Perverse pullbacks
Adeel A. Khan, Tasuki Kinjo, Hyeonjun Park +1
We define a new perverse t-exact pullback operation on derived categories of constructible sheaves which generalizes most perverse t-exact functors in sheaf theory, such as microlo…
Elliptic loop spaces
Emile Bouaziz, Adeel A. Khan
We introduce an elliptic avatar of loop spaces in derived algebraic geometry, completing the familiar trichotomoy of rational, trigonometric and elliptic objects. Heuristically, th…
Lisse extensions of weaves
Adeel A. Khan
Any sheaf theory on schemes extends canonically to Artin stacks via a procedure called lisse extension. In this paper we show that lisse extension preserves the formalism of Grothe…
Modularity of higher theta series II: Chow group of the generic fiber
Tony Feng, Adeel A. Khan
Higher theta series on moduli spaces of Hermitian shtukas were constructed by Feng--Yun--Zhang and conjectured to be modular, parallel to classical conjectures in the Kudla program…
The derived homogeneous Fourier transform
Adeel A. Khan
We study a derived version of Laumon's homogeneous Fourier transform, which exchanges G_m-equivariant sheaves on a derived vector bundle and its dual. In this context, the Fourier…
Lectures on algebraic stacks
Adeel A. Khan
Notes on algebraic stacks, prepared for an 11-lecture course at the NCTS, Taipei, during the fall of 2022.