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Motivic Cohomology, K-Theory and Topological Cyclic Homology

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Abstract

We give a survey onmotivic cohomology, higher algebraic K-theory, and topological cyclic homology. We concentrate on results which are relevant for applications in arithmetic algebraic geometry (in particular, we do not discuss non-commutative rings), and our main focus lies on sheaf theoretic results for smooth schemes, which then lead to global results using local-to-global methods.

Keywords

  • Irreducible Component
  • Spectral Sequence
  • Homotopy Group
  • Discrete Valuation Ring
  • Minimal Prime Ideal

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Geisser, T. (2005). Motivic Cohomology, K-Theory and Topological Cyclic Homology. In: Friedlander, E., Grayson, D. (eds) Handbook of K-Theory. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27855-9_6

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