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dc.contributor.author
Fouvry, Étienne
dc.contributor.author
Kowalski, Emmanuel
dc.contributor.author
Michel, Philippe
dc.date.accessioned
2021-11-11T06:52:32Z
dc.date.available
2021-11-10T14:49:04Z
dc.date.available
2021-11-11T06:52:32Z
dc.date.issued
2021
dc.identifier.issn
0240-2963
dc.identifier.issn
2258-7519
dc.identifier.other
10.5802/afst.1671
en_US
dc.identifier.uri
http://hdl.handle.net/20.500.11850/514687
dc.identifier.doi
10.3929/ethz-b-000514687
dc.description.abstract
In the analytic study of trace functions of ℓ-adic sheaves over finite fields, a crucial issue is to control the conductor of sheaves constructed in various ways. We consider cohomological transforms on the affine line over a finite field which have trace functions given by linear operators with an additive character of a rational function in two variables as a kernel. We prove that the conductor of such transforms is bounded in terms of the complexity of the input sheaf and of the rational function defining the kernel, and discuss applications of this result, including motivating examples arising from the Polymath8 project.
en_US
dc.format
application/pdf
en_US
dc.language.iso
en
en_US
dc.publisher
Université Toulouse
en_US
dc.rights.uri
http://creativecommons.org/licenses/by/4.0/
dc.subject
Étale cohomology
en_US
dc.subject
Conductor
en_US
dc.subject
l-adic sheaves
en_US
dc.subject
Riemann hypothesis over finite fields
en_US
dc.subject
Exponential sums
en_US
dc.title
On the conductor of cohomological transforms
en_US
dc.type
Journal Article
dc.rights.license
Creative Commons Attribution 4.0 International
dc.date.published
2021-05-25
ethz.journal.title
Annales de la Faculté des Sciences de Toulouse. Mathématiques
ethz.journal.volume
30
en_US
ethz.journal.issue
1
en_US
ethz.pages.start
203
en_US
ethz.pages.end
254
en_US
ethz.version.deposit
publishedVersion
en_US
ethz.grant
Geometric and Analytic Number Theory
en_US
ethz.publication.place
Toulouse
en_US
ethz.publication.status
published
en_US
ethz.leitzahl
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02003 - Mathematik Selbständige Professuren::03796 - Kowalski, Emmanuel / Kowalski, Emmanuel
en_US
ethz.leitzahl.certified
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02003 - Mathematik Selbständige Professuren::03796 - Kowalski, Emmanuel / Kowalski, Emmanuel
en_US
ethz.grant.agreementno
153647
ethz.grant.fundername
SNF
ethz.grant.funderDoi
10.13039/501100001711
ethz.grant.program
Projektförderung in Mathematik, Natur- und Ingenieurwissenschaften (Abteilung II)
ethz.date.deposited
2021-11-10T14:49:10Z
ethz.source
FORM
ethz.eth
yes
en_US
ethz.availability
Open access
en_US
ethz.rosetta.installDate
2021-11-11T06:52:38Z
ethz.rosetta.lastUpdated
2021-11-11T06:52:38Z
ethz.rosetta.exportRequired
true
ethz.rosetta.versionExported
true
ethz.COinS
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