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On Dynamical Systems and Their Possible Significance for Arithmetic Geometry

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Regulators in Analysis, Geometry and Number Theory

Part of the book series: Progress in Mathematics ((PM,volume 171))

Abstract

In the papers [D1], [D5], [D3] a cohomological formalism for algebraic schemes X 0 over spec ℤ or spec ℚ was conjectured which would explain many of the expected properties of motivic L-series. All consequences of this very rigid formalism that I could imagine turned out to be either provable [D2], [D4], [DN], [Sa] or to amount to some well known conjectures on L-series of motives, as for example the Riemann hypotheses and the Artin conjecture—both generalized to the context of motives—and the Bloch Beilinson conjectures on vanishing orders.

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Author information

Authors and Affiliations

  1. Mathematisches Institut, Einsteinstraße 62, 48149, Münster, Germany

    Christopher Deninger

Authors
  1. Christopher Deninger
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Editor information

Editors and Affiliations

  1. Department of Mathematical Sciences, University of Durham, Durham, DH1 3LE, UK

    Alexander Reznikov

  2. UFR Mathématiques et Informatique, ULP, 67084, Strasbourg Cedex, France

    Norbert Schappacher

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Deninger, C. (2000). On Dynamical Systems and Their Possible Significance for Arithmetic Geometry. In: Reznikov, A., Schappacher, N. (eds) Regulators in Analysis, Geometry and Number Theory. Progress in Mathematics, vol 171. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1314-7_3

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  • DOI: https://doi.org/10.1007/978-1-4612-1314-7_3

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-7089-8

  • Online ISBN: 978-1-4612-1314-7

  • eBook Packages: Springer Book Archive

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