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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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Isogenies, Connectedness, and Lie-Irreducibility

Isogenies, Connectedness, and Lie-Irreducibility

(p.45) Chapter 8Isogenies, Connectedness, and Lie-Irreducibility
Convolution and Equidistribution

Nicholas M. Katz

Princeton University Press

This chapter takes up the proofs of Theorems 8.1 and 8.2. For each prime to p integer n, we have the n'th power homomorphism [n] : G → G. Formation of the direct image is an exact functor from Perv to itself, which maps Neg to itself, in Ƿ to itself, and which (because a homomorphism) is compatible with middle convolution. So for a given object N in Garith, [n]* allows us to view 〈Narith as a Tannakian subcategory of 〈[n]*Narith, and 〈Ngeom as a Tannakian subcategory of 〈[n]*Ngeom.

Keywords:   number theory, isogenies, connectedness, lie-irreducibility, Tannakian groups

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