Journal of the Ramanujan Mathematical Society

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On the Norm Principle for Quadratic Forms


Affiliations
1 Ecole Polytechnique Federale De Lausanne, Institut De Geometrie, Algebre Et Topologie, Batiment BCH, Lausanne 1015, Switzerland
2 St. Petersburg Department of V.A. Steklov Institute of Mathematics, 27, Fontanka, St. Petersburg 191023, Russian Federation
3 Fakultat Fur Mathematik, Universitat Bielefeld, Postfach 100131, Bielefeld 33501, Germany
     

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We prove a version of Knebusch’s norm principle for finite etale extensions of semi-local noetherian domains with infinite residue fields of characteristic different from 2. As an application we prove Grothendieck’s conjecture on principal homogeneous spaces for the spinor group of a quadratic space.
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  • On the Norm Principle for Quadratic Forms

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Authors

M. Ojanguren
Ecole Polytechnique Federale De Lausanne, Institut De Geometrie, Algebre Et Topologie, Batiment BCH, Lausanne 1015, Switzerland
I. Panin
St. Petersburg Department of V.A. Steklov Institute of Mathematics, 27, Fontanka, St. Petersburg 191023, Russian Federation
K. Zainoulline
Fakultat Fur Mathematik, Universitat Bielefeld, Postfach 100131, Bielefeld 33501, Germany

Abstract


We prove a version of Knebusch’s norm principle for finite etale extensions of semi-local noetherian domains with infinite residue fields of characteristic different from 2. As an application we prove Grothendieck’s conjecture on principal homogeneous spaces for the spinor group of a quadratic space.