Two-dimensional Idèles with Cycle Module Coefficients
arXiv:1101.0424 · doi:10.1002/mana.201300230
Abstract
We give a theory of idèles with coefficients for smooth surfaces over a field. It is an analogue of Beilinson/Huber's theory of higher adèles, but handling cycle module sheaves instead of quasi-coherent ones. We prove that they give a flasque resolution of the cycle module sheaves in the Zariski topology. As a technical ingredient we show the Gersten property for cycle modules on equicharacteristic complete regular local rings, which might be of independent interest.
major change in exposition, streamlined, removed incorrect claim about product map (many thanks to S. Gorchinskiy for pointing this out to me), bibliography updated