Two-dimensional Id\`eles with Cycle Module Coefficients
Number Theory
2019-03-18 v2 K-Theory and Homology
Abstract
We give a theory of id\`eles with coefficients for smooth surfaces over a field. It is an analogue of Beilinson/Huber's theory of higher ad\`eles, 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.
Cite
@article{arxiv.1101.0424,
title = {Two-dimensional Id\`eles with Cycle Module Coefficients},
author = {Oliver Braunling},
journal= {arXiv preprint arXiv:1101.0424},
year = {2019}
}
Comments
major change in exposition, streamlined, removed incorrect claim about product map (many thanks to S. Gorchinskiy for pointing this out to me), bibliography updated