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Volume 105 - Issue 3 - February 1997

Contents

Research Article

  • Fano threefolds in positive characteristic

  • N. I. SHEPHERD-BARRON
  • Published online by Cambridge University Press:
    04 December 2007, pp. 237-265
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  • We show that the birational classification in positive characteristic of smooth Fano threefolds $X$ with Picard number 1 is the same as in characteristic zero. In particular, there are no exotic such Fanos; as a consequence of the classification, $X$ is shown to be liftable without ramification to characteristic zero and to contain a line. The main techniques employed are those of Ekedahl and of Mori and Takeuchi.

  • Sur la cohomologie à supports compacts des variétés de Shimura pour GSp(4)$_{\bb Q}$

  • GÉRARD LAUMON
  • Published online by Cambridge University Press:
    04 December 2007, pp. 267-359
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  • In this paper we compute the cohomology with compact supports of a Siegel threefold as a virtual module over the product of the Galois group of$\bar{\bb Q}$ over ${\bb Q}$ and the Hecke algebra. We use a method which has been developed by Ihara, Langlands and Kottwitz: comparison of the Grothendieck—Lefschetz formula and the Arthur—Selberg trace formula.