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2 results

  • Cohomological Approach to Class Field Theory in Arithmetic Topology

  • Part of
  • Tomoki Mihara
  • Journal:
    Canadian Journal of Mathematics / Volume 71 / Issue 4 / August 2019
    Published online by Cambridge University Press:
    09 January 2019, pp. 891-935
    Print publication:
    August 2019
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  • We establish class field theory for three-dimensional manifolds and knots. For this purpose, we formulate analogues of the multiplicative group, the idèle class group, and ray class groups in a cocycle-theoretic way. Following the arguments in abstract class field theory, we construct reciprocity maps and verify the existence theorems.

  • Utilisation d’une cohomologie étale équivariante en topologie arithmétique

  • Part of
  • Baptiste Morin
  • Journal:
    Compositio Mathematica / Volume 144 / Issue 1 / January 2008
    Published online by Cambridge University Press:
    01 January 2008, pp. 32-60
    Print publication:
    January 2008
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  • Sikora has given results which confirm the analogy between number fields and 3-manifolds. However, he has given proofs of his results which are very different in the arithmetic and in the topological case. In this paper, we show how to provide a unified approach to the results in the two cases. For this we introduce an equivariant cohomology which satisfies a localization theorem. In particular, we obtain a satisfactory explanation for the coincidences between Sikora’s formulas which leads us to clarify and to extend the dictionary of arithmetic topology.