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Convolution and EquidistributionSato-Tate Theorems for Finite-Field Mellin Transforms (AM-180)$
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Nicholas M. Katz

Print publication date: 2012

Print ISBN-13: 9780691153308

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691153308.001.0001

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Symplectic Examples

Symplectic Examples

(p.89) Chapter 18 Symplectic Examples
Convolution and Equidistribution

Nicholas M. Katz

Princeton University Press

This chapter works on either the split or the nonsplit form. It begins with a lisse sheaf Ƒ on a dense open set j : UG which is geometrically irreducible, pure of weight zero, and not geometrically isomorphic to (the restriction to U of) any Kummer sheaf Lᵪ. It denotes by G := j*Ƒ its middle extension to G. Then the object N := G(1/2)[1] ɛ Garith is pure of weight zero and geometrically irreducible.

Keywords:   number theory, split form, nonsplit form

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