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arXiv · 1209.2068

A plethora of inertial products

Dan Edidin·Tyler J. Jarvis·Takashi Kimura
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Abstract

For a smooth Deligne-Mumford stack X we describe a large number of inertial products on K(IX) and A*(IX) and corresponding inertial Chern characters. We do this by developing a theory of inertial pairs. Each inertial pair determines an inertial product on K(IX) and an inertial product on A*(IX) and Chern character ring homomorphisms between them. We show that there are many inertial pairs; indeed, every vector bundle V on X defines two new inertial pairs. We recover, as special cases, the orbifold products of Chen-Run, Abramovich-Graber-Vistoli, Jarvis-Kaufmann-Kimura, and Edidin-Jarvis-Kimura and the virtual product of Gonzalez-Lupercio-Segovia-Uribe-Xicotencatl. We also introduce an entirely new product we call the localized orbifold product, which is defined on the complexification of K(IX). The inertial products developed in this paper are used in a subsequent paper to describe a theory of inertial Chern classes and power operations in inertial K-theory. These constructions provide new manifestations of mirror symmetry, in the spirit of the Hyper-Kaehler Resolution Conjecture.

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Dan Edidin, Tyler J. Jarvis, Takashi Kimura. 2015-01-27. A plethora of inertial products. https://doi.org/10.2140/akt.2016.1.85

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