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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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GL(n) Examples

GL(n) Examples

Chapter:
(p.81) Chapter 17 GL(n) Examples
Source:
Convolution and Equidistribution
Author(s):

Nicholas M. Katz

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691153308.003.0018

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 LRᵪ. 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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