Proves Toda's chi-independence conjecture and identifies BPS Lie algebra with tautological classes for one-dimensional Mukai vectors using Hecke operators and bialgebra structures.
Khan, Virtual fundamental classes for derived stacks I
5 Pith papers cite this work, alongside 16 external citations. Polarity classification is still indexing.
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abstract
We construct the \'etale motivic Borel-Moore homology of derived Artin stacks. Using a derived version of the intrinsic normal cone, we construct fundamental classes of quasi-smooth derived Artin stacks and demonstrate functoriality, base change, excess intersection, and Grothendieck-Riemann-Roch formulas. These classes also satisfy a general cohomological B\'ezout theorem which holds without any transversity hypotheses. The construction is new even for classical stacks and as one application we extend Gabber's proof of the absolute purity conjecture to Artin stacks.
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math.AG 5representative citing papers
A general descendability criterion for topological six-functor formalisms yields h-descent for étale motivic spectra and rational motivic cohomology, plus arc-descent in weights ≤1.
Logarithmic Hochschild homology is functorial for strong log Fourier-Mukai transforms on smooth proper log pairs, yielding a dg bicategory of logarithmic correspondences with compatible Chern characters and Euler pairings.
An analogous Pardon homology algebra is defined for zero-cycles in d-folds, supplying a new perspective on point-counting enumerative problems including the degree-zero MNOP conjecture.
Lecture notes covering the theory of algebraic stacks for an 11-lecture graduate course.
citing papers explorer
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Hecke operators on symplectic surfaces and $\chi$-independence
Proves Toda's chi-independence conjecture and identifies BPS Lie algebra with tautological classes for one-dimensional Mukai vectors using Hecke operators and bialgebra structures.
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Descendability and descent in topological weaves
A general descendability criterion for topological six-functor formalisms yields h-descent for étale motivic spectra and rational motivic cohomology, plus arc-descent in weights ≤1.
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Functoriality of logarithmic Hochschild homology of log smooth pairs
Logarithmic Hochschild homology is functorial for strong log Fourier-Mukai transforms on smooth proper log pairs, yielding a dg bicategory of logarithmic correspondences with compatible Chern characters and Euler pairings.
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A Pardon Algebra for Zero-cycles
An analogous Pardon homology algebra is defined for zero-cycles in d-folds, supplying a new perspective on point-counting enumerative problems including the degree-zero MNOP conjecture.
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Lectures on algebraic stacks
Lecture notes covering the theory of algebraic stacks for an 11-lecture graduate course.