"Inertial Chow rings and a new asymptotic product"

Abstract: For any toric Deligne-Mumford stack X and equivariant vector bundle V, we can define an associative inertial product ★. We give a ring presentation for the inertial Chow ring of X under ★ and show how to compute it in the toric case. In particular, we make explicit distinctions between the contributions of the inertia of X and of the product ★. We further show the existence of a new associative product on the inertia of X in which the rank of V asymptotically approaches infinity, and we compute its Chow ring.