SU\G(𝔸)/K·U

Hypersurfaces and the Weil Conjectures

A. J. Scholl

Type: Article

Publication Date: 2010-05-28

Citations: 3

DOI: https://doi.org/10.1093/imrn/rnq098

Abstract

We give a proof that the Riemann hypothesis for hypersurfaces over finite fields implies the result for all smooth proper varieties, by a deformation argument which does not use the theory of Lefschetz pencils or the l-adic Fourier transform.

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  • International Mathematics Research Notices - View
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Works Cited by This (10)

Action Title Year Authors
+ ON THE NUMBER OF POINTS OF A HYPERELLIPTIC CURVE OVER A FINITE PRIME FIELD 1969 S. A. Stepanov
+ Limits of Hodge structures 1976 J. H. M. Steenbrink
+ La conjecture de Weil. I 1974 Pierre Deligne
+ PDF Chat Smoothness, semi-stability and alterations 1996 A. J. de Jong
+ WEIGHT SPECTRAL SEQUENCES AND INDEPENDENCE OF $\ell$ 2003 Takeshi Saito
+ PDF Chat Families of curves and alterations 1997 A. J. de Jong
+ The Motivic Vanishing Cycles and the Conservation Conjecture 2007 Joseph Ayoub
+ �ber die lokale Zetafunktion von Shimuravariet�ten. Monodromiefiltration und verschwindende Zyklen in ungleicher Charakteristik 1982 Michael Rapoport
Th. Zink
+ Théorie de Hodge I 1970 Pierre Deligne
+ La Conjecture de Weil. II 1980 Pierre Deligne