Inertial Chow rings and a new asymptotic product
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For any toric Deligne-Mumford stack X and equivariant vector bundle V , we can define an two associative inertial products. We give a ring presentation for the inertial Chow ring of X under each of these products and compute these rings in the toric case. In particular, we make explicit distinctions between the contributions of the inertia of X and of the products themselves. 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.