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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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Frobenius Tori and Weights; Getting Elements of Garith

Frobenius Tori and Weights; Getting Elements of Garith

Chapter:
(p.77) Chapter 16 Frobenius Tori and Weights; Getting Elements of Garith
Source:
Convolution and Equidistribution
Author(s):

Nicholas M. Katz

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691153308.003.0017

This chapter works on Gₘ/k. It considers an arithmetically semisimple object N ɛ Garith which is pure of weight zero. It assumes it is of the form G[1], with G a middle extension sheaf. Thus, for some open set j : U ⊂ 𝔾ₘ, we have G = j*Ƒ, for Ƒ := j*G a lisse sheaf on U which is pure of weight −1 and arithmetically semisimple, and having no geometric constituent isomorphic to a Kummer sheaf.

Keywords:   number theory, semisimple object, pure weight, Frobenius tori

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