Hall algebras of coherent sheaves on toric varieties over F_1.
Abstract
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.