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Bloch-Kato Conjecture and Motivic Cohomology with Finite Coefficients

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The Arithmetic and Geometry of Algebraic Cycles

Part of the book series: NATO Science Series ((ASIC,volume 548))

Abstract

In this paper we show that the Beilinson-Lichtenbaum Conjecture which describes motivic cohomology of (smooth) varieties with finite coefficients is equivalent to the Bloch-Kato Conjecture, relating Milnor K-theory to Galois cohomology. The latter conjecture is known to be true in weight 2 for all primes [M-S] and in all weights for the prime 2 [V 3].

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Suslin, A., Voevodsky, V. (2000). Bloch-Kato Conjecture and Motivic Cohomology with Finite Coefficients. In: Gordon, B.B., Lewis, J.D., Müller-Stach, S., Saito, S., Yui, N. (eds) The Arithmetic and Geometry of Algebraic Cycles. NATO Science Series, vol 548. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4098-0_5

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  • DOI: https://doi.org/10.1007/978-94-011-4098-0_5

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-0-7923-6194-7

  • Online ISBN: 978-94-011-4098-0

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