Vol. 3, No. 1, 2018

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Suslin's moving lemma with modulus

Wataru Kai and Hiroyasu Miyazaki

Vol. 3 (2018), No. 1, 55–70

The moving lemma of Suslin (also known as the generic equidimensionality theorem) states that a cycle on X × An meeting all faces properly can be moved so that it becomes equidimensional over An. This leads to an isomorphism of motivic Borel–Moore homology and higher Chow groups.

In this short paper we formulate and prove a variant of this. It leads to a modulus version of the isomorphism, in an appropriate pro setting.

Chow group, modulus, moving lemma
Mathematical Subject Classification 2010
Primary: 14C25
Secondary: 19E15
Received: 19 April 2016
Revised: 31 October 2016
Accepted: 7 March 2017
Published: 7 September 2017
Wataru Kai
Fakultät für Mathematik
Universität Duisburg-Essen
D-45127 Essen
Hiroyasu Miyazaki
Graduate School of Mathematical Sciences
University of Tokyo
Tokyo 153-8914