Two-dimensional Idèles with Cycle Module Coefficients

Details Two-dimensional Idèles with Cycle Module Coefficients Two-dimensional Idèles with Cycle Module Coefficients

2011-01-02

arxiv.org/abs/1101.0424v1

Mathematics

Number Theory

Scientific paper

We give a flasque resolution of the Zariski sheaves of Rost cycle modules in terms of 2-dimensional complete id\`eles on surfaces. We give explicit formulas relating this id\`ele resolution with the Gersten-type and \v{C}ech resolution. As an application we recover an old formula expressing intersection multiplicities in terms of tame symbols and a \v{C}ech analogue thereof. We show that this approach is workable for explicit computations.

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