COHA of surfaces and factorization algebras


Kapranov, M. (2019). COHA of surfaces and factorization algebras. Perimeter Institute. https://pirsa.org/19020077


Kapranov, Mikhail. COHA of surfaces and factorization algebras. Perimeter Institute, Feb. 25, 2019, https://pirsa.org/19020077


          @misc{ pirsa_PIRSA:19020077,
            doi = {10.48660/19020077},
            url = {https://pirsa.org/19020077},
            author = {Kapranov, Mikhail},
            keywords = {Mathematical physics},
            language = {en},
            title = {COHA of surfaces and factorization algebras},
            publisher = {Perimeter Institute},
            year = {2019},
            month = {feb},
            note = {PIRSA:19020077 see, \url{https://pirsa.org}}

Mikhail Kapranov University of Tokyo


This is a report on joint work with E. Vasserot. For a smooth quasiprojective surface S we consider the stack Coh(S) of coherent sheaves on S with compact support and make the Borel-Moore homology of Coh(S) into an associative algebra using a derived version of the Hall multiplication diagram. Subcategories in Coh(S) given by various conditions on dimension of support give rise to various types of Hecke operators. In particular, we consider the COHA R(S) of sheaves with 0-dimensional support and show that its chain level lift is a factorization coalgebra on S with values in homotopy associative algebras. This allows us to find the size (graded dimension) of R(S).