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Arithmetic cycles on Picard modular surfaces and modular forms of Nebentypus

1985
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Journal für die Reine und Angewandte Mathematik
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We develop a localized intersection theory for arithmetic schemes on the model of Fulton's intersection theory. We prove a Lefschetz ¢xed 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. Let S peR be the spectrum of a characteristic 0 complete discrete valuation ring R with algebraically closed residue ¢eld k of characteristic p b 0 and fraction

doi:10.1515/crll.1985.357.115
fatcat:sq6zhwzwtzcbbfzfbv5g3gev5a