On the Reciprocity Sequence in the Higher Class Field Theory of Function Fields

Part of the NATO ASI Series book series (ASIC, volume 407)


According to a conjecture of Kato (1986), the classical reciprocity sequence for the Brauer group of a function field in one variable over a finite field F should have analogues for higher dimensional function fields. A more precise form of the conjecture is that on smooth projective varieties of dimension d over F, the homology of a certain Bloch-Ogus complex of length d + 1 should be trivial except in the last term, where it should be ℚ/ℤ. For surfaces, the conjecture was established some years ago. In the present paper, I prove that for varieties of arbitrary dimension, the complex has the expected homology in its last four terms, thus settling the case of threefolds (attention is restricted to torsion prime to the characteristic).


Exact Sequence Spectral Sequence Finite Field Residue Field Torsion Group 
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© Springer Science+Business Media Dordrecht 1993

Authors and Affiliations

  1. 1.C.N.R.S., URA D0752Université de Paris-SudOrsay CédexFrance

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