• Corpus ID: 119162219

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… 
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