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On equivariant derived categories
We study the equivariant category associated to a finite group action on the derived category of coherent sheaves of a smooth projective variety. In...
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Existence of moduli spaces for algebraic stacks
We provide necessary and sufficient conditions for when an algebraic stack admits a good moduli space and prove a semistable reduction theorem for...
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On the cohomology of character stacks for non-orientable surfaces
We give a counterexample to a formula suggested by the work of Letellier and Rodriguez-Villegas (Ann l’Inst Fourier 36, 2022) for the mixed Poincaré...
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Serre duality for tame Deligne–Mumford stacks
Using the exceptional inverse image functor for quasi-finite proper morphisms of separated tame Deligne–Mumford stacks of finite type over a field k ,...
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Equivariant Burnside groups and representation theory
We apply the equivariant Burnside group formalism to distinguish linear actions of finite groups, up to equivariant birationality. Our approach is...
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Equivariant eta forms and equivariant differential K-theory
In this paper, for a compact Lie group action, we prove the anomaly formula and the functoriality of the equivariant Bismut-Cheeger eta forms with...
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K-theory and G-theory of derived algebraic stacks
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...
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Birational classification of toric orbifolds
We give a complete classification of the torus-equivariant birational equivalence classes of smooth proper toric Deligne–Mumford stacks with trivial...
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Stacks for Everyone Who Cares About Varieties and Singularities
Algebraic geometry is about the geometry of varieties. Anything else is meant to help in understanding the geometry of varieties, and must be...
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Virtual Riemann–Roch theorems for almost perfect obstruction theories
This is the third in a series of works devoted to constructing virtual structure sheaves and K -theoretic invariants in moduli theory. The central...
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Symbols and Equivariant Birational Geometry in Small Dimensions
We discuss the equivariant Burnside group and related new invariants in equivariant birational geometry, with a special emphasis on applications in...
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PROJECTIVE GENERATION FOR EQUIVARIANT -MODULES
We investigate compact projective generators in the category of equivariant
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