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ÉTALE MOTIVIC COHOMOLOGY AND ALGEBRAIC CYCLES

Part of: $K$-theory in geometry

Published online by Cambridge University Press:  24 November 2014

Andreas Rosenschon  and
V. Srinivas
Andreas Rosenschon
Affiliation:
Mathematisches Institut, Ludwigs Maximilians Universität, München, Germany (axr@math.lmu.de)
V. Srinivas
Affiliation:
School of Mathematics, Tata Institute of Fundamental Research, Mumbai, India (srinivas@math.tifr.res.in)
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Abstract

We consider étale motivic or Lichtenbaum cohomology and its relation to algebraic cycles. We give an geometric interpretation of Lichtenbaum cohomology and use it to show that the usual integral cycle maps extend to maps on integral Lichtenbaum cohomology. We also show that Lichtenbaum cohomology, in contrast to the usual motivic cohomology, compares well with integral cohomology theories. For example, we formulate integral étale versions of the Hodge and the Tate conjecture, and show that these are equivalent to the usual rational conjectures.

Keywords

motivic cohomologyalgebraic cycles

MSC classification

Primary: 19E15: Algebraic cycles and motivic cohomology
Secondary: 19E20: Relations with cohomology theories
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 15 , Issue 3 , July 2016 , pp. 511 - 537
Copyright
© Cambridge University Press 2014 

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