# The cohomological Hall algebra of a surface and factorization cohomology

@article{Kapranov2019TheCH, title={The cohomological Hall algebra of a surface and factorization cohomology}, author={Mikhail M. Kapranov and Eric Vasserot}, journal={arXiv: Algebraic Geometry}, year={2019} }

For a smooth quasi-projective surface S over complex numbers we consider the Borel-Moore homology of the stack of coherent sheaves on S with compact support and make this space into an associative algebra by a version of the Hall multiplication. This multiplication involves data (virtual pullbacks) governing the derived moduli stack, i.e., the perfect obstruction theory naturally existing on the non-derived stack. By restricting to sheaves with support of given dimension, we obtain several…

## 28 Citations

Categorification of two-dimensional cohomological Hall algebras

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In the present paper, we provide a full categorification, at the level of stable $\infty$-categories, of two-dimensional cohomological Hall algebras of curves and surfaces. This is achieved by…

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. We introduce a version of the P=W conjecture relating the Borel– Moore homology of the stack of representations of the fundamental group of a genus g Riemann surface with the Borel–Moore homology…

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We show that the categorified cohomological Hall algebra structures on surfaces constructed by Porta-Sala descend to those on Donaldson-Thomas categories on local surfaces introduced in the author's…

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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…

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For any free oriented Borel–Moore homology theory A , we construct an associative product on the A -theory of the stack of Higgs torsion sheaves over a projective curve C . We show that the resulting…

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In the present paper, we provide a full categorification, at the level of stable $\infty$-categories, of two-dimensional cohomological Hall algebras of curves and surfaces. This is achieved by…

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