Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-25T05:27:55.014Z Has data issue: false hasContentIssue false
  • English
  • Français

Majoration de sommes trigonométriques modulo pn

Published online by Cambridge University Press:  04 December 2007

MOUSSA SAÏBI
MOUSSA SAÏBI
Affiliation:
Faculté de Mathéematiques et d‘Informatique, Université de Picardie Jules Verne 33, Rue Saint Leu, 80039 Amiens Cedex, France e-mail: saï[email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We give a generic estimation of trigonometric sums defined over closed sub-schemes with semi-stable reduction of the standard affine scheme modulo pn(n [ges ] 2). We use Greenberg realisation to reduce to trigonometric sums defined over smooths sub-schemes of a finite product of Witt vectors over the finite field of p elements. Using the cohomological interpretation of this sums over a finite field, the sum is directly related to the Fourier–Deligne transformation of the dual pairs of Witt vectors. We deduce the estimation from the properties of the Fourier–Deligne transformation on simple perverse sheaves and pure sheaves.

Keywords

Fourier-Deligne transformationWitt vectorsGreenberg realisationtrigonometric sums.
Type
Research Article
Information
Compositio Mathematica , Volume 116 , Issue 3 , May 1999 , pp. 311 - 319
Copyright
© 1999 Kluwer Academic Publishers