• 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}
}
• Published 22 January 2019
• Mathematics
• arXiv: Algebraic Geometry
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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