Abstract
We develop a localized intersection theory for arithmetic schemes on the model of Fulton's intersection theory. We prove a Lefschetz fixed point formula for arithmetic surfaces, and give an application to a conjecture of Serre on the existence of Artin's representations for regular local rings of dimension 2 and unequal characteristic.
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Abbes, A. Cycles on Arithmetic Surfaces. Compositio Mathematica 122, 23–111 (2000). https://doi.org/10.1023/A:1001822419774
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DOI: https://doi.org/10.1023/A:1001822419774