By Uwe Jannsen, Steven L. Kleiman, Jean Pierre Serre

Explanations have been brought within the mid-1960s by means of Grothendieck to give an explanation for the analogies one of the numerous cohomology theories for algebraic types, to play the function of the lacking rational cohomology, and to supply a blueprint for proving Weil's conjectures abou the zeta functionality of a range over a finite box. over the past ten years or so, researchers in numerous parts - Hodge concept, algebraic okay -theory, polylogarithms, automorphic types, L -functions, trigonometric sums, and algebraic cycles - have stumbled on that an enlarged (and partially conjectural) idea of "mixed" reasons shows and explains phenomena showing in each one region. hence the idea holds the opportunity of enriching and unifying those parts. those volumes comprise the revised texts of approximately the entire lectures offered a the AMS-IMS-SIAM Joint summer time examine convention on reasons, held in Seattle in 1991. a couple of comparable works ae additionally integrated, making for a complete of forty-seven papers, from common introductions to really good surveys to investigate papers. This ebook is meant for learn mathematicians.

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