2000 | OriginalPaper | Chapter
On Dynamical Systems and Their Possible Significance for Arithmetic Geometry
Author : Christopher Deninger
Published in: Regulators in Analysis, Geometry and Number Theory
Publisher: Birkhäuser Boston
Included in: Professional Book Archive
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In the papers [D1], [D5], [D3] a cohomological formalism for algebraic schemes X0 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.