Hall algebras of coherent sheaves on toric varieties over F_1.

7 March 2018
Prof. Matt Szczesny
Hall algebras of categories of quiver representations and coherent sheaves on smooth projective curves over F_q recover interesting representation-theoretic objects such as quantum groups and their generalizations. I will define and describe the structure of the Hall algebra of coherent sheaves on a projective variety over F_1, with P^2 as the main example. Examples suggest that it should be viewed as a degenerate q->1 limit of its counterpart over F_q.