New York Journal of Mathematics
Volume 19 (2013) 545-564


O. Braunling

Bad intersections and constructive aspects of the Bloch-Quillen formula

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Published: September 2, 2013
Keywords: intersection, Bloch-Quillen, Milnor K-theory
Subject: Primary 14C35; Secondary 14C17

The Bloch-Quillen formula, especially a version with Milnor K-coefficients, makes it possible to express the product of the Chow ring through an ordinary cup product in sheaf cohomology and the concatenation product of symbols. No special care is needed if cycles do not intersect properly, no moving lemma nor deformation to the normal cone. We give an explicit formula for the intersection form along this line, different from the Serre Tor-formula.


This work has been supported by the DFG SFB/TR45. Periods, moduli spaces, and arithmetic of algebraic varieties.

Author information

Fakultät für Mathematik, Universität Duisburg-Essen, Thea-Leymann-Strasse 9, 45127 Essen, Germany