Some years ago a conference on l-adic cohomology in Oberwolfach was
held with the aim of reaching an understanding of Deligne's proof
of the Weil conjec tures. For the convenience of the speakers the
present authors - who were also the organisers of that meeting -
prepared short notes containing the central definitions and ideas
of the proofs. The unexpected interest for these notes and the
various suggestions to publish them encouraged us to work somewhat
more on them and fill out the gaps. Our aim was to develop the
theory in as self contained and as short a manner as possible. We
intended especially to provide a complete introduction to etale and
l-adic cohomology theory including the monodromy theory of
Lefschetz pencils. Of course, all the central ideas are due to the
people who created the theory, especially Grothendieck and Deligne.
The main references are the SGA-notes 64-69]. With the kind
permission of Professor J. A. Dieudonne we have included in the
book that finally resulted his excellent notes on the history of
the Weil conjectures, as a second introduction. Our original notes
were written in German. However, we finally followed the
recommendation made variously to publish the book in English. We
had the good fortune that Professor W. Waterhouse and his wife
Betty agreed to translate our manuscript. We want to thank them
very warmly for their willing involvement in such a tedious task.
We are very grateful to the staff of Springer-Verlag for their
careful work."
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