MOTMELSUM

Motivic Mellin transforms and exponential sums through non-archimedean geometry

 Coordinatore CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE 

Spiacenti, non ci sono informazioni su questo coordinatore. Contattare Fabio per maggiori infomrazioni, grazie.

 Nazionalità Coordinatore France [FR]
 Totale costo 912˙000 €
 EC contributo 912˙000 €
 Programma FP7-IDEAS-ERC
Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013)
 Code Call ERC-2013-CoG
 Funding Scheme ERC-CG
 Anno di inizio 2014
 Periodo (anno-mese-giorno) 2014-03-01   -   2019-02-28

 Partecipanti

# participant  country  role  EC contrib. [€] 
1    CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE

 Organization address address: Rue Michel -Ange 3
city: PARIS
postcode: 75794

contact info
Titolo: Mrs.
Nome: Bénédicte
Cognome: Samyn
Email: send email
Telefono: +33 320125807
Fax: +33 320630043

FR (PARIS) hostInstitution 912˙000.00
2    CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE

 Organization address address: Rue Michel -Ange 3
city: PARIS
postcode: 75794

contact info
Titolo: Prof.
Nome: Raf
Cognome: Cluckers
Email: send email
Telefono: +33 3 20434193
Fax: +33 3 20434302

FR (PARIS) hostInstitution 912˙000.00

Mappa


 Word cloud

Esplora la "nuvola delle parole (Word Cloud) per avere un'idea di massima del progetto.

motivic    summation    fourier    formulas    sums    multiplicative    local    characters    transforms    theory    exponential    varies    uniform    mellin    group    igusa    additive    transfer    principles    poisson   

 Obiettivo del progetto (Objective)

'We aim to create a new and powerful theory of motivic integration which incorporates Mellin transforms. The absence of motivic Mellin transforms is a major drawback of the existing theories. Classical Mellin transforms are in essence Fourier transforms on the multiplicative group of local fields. We aim to apply this theory to study new motivic Poisson summation formulas, new transfer principles, and applications of these. All of this has so far only been studied in the presence of additive characters, and remains completely open for multiplicative characters. Understanding all this at a motivic level yields a uniform understanding when the local field varies and will require an approach using non-archimedean geometry. We will open up possibilities for applications via new transfer principles and will give access to motivic Poisson formulas of other groups than the additive group. For these applications it is important that Fubini Theorems are present at the level of the motivic integrals, which we aim to develop. We will overcome the major obstacle of the totally different nature of the dual group of the multiplicative group by a proposed sequence of germs of ideas by the author. The importance of our work on motivic Fourier transforms on the additive group is already widely recognized, and this proposal will complement it by exploring the new territory of motivic multiplicative characters. A final topic is the study of the highly non-understood exponential sums modulo powers of primes, in relation with Igusa's foundational work. We will try to discover a deeper understanding of the uniform behavior of these sums when the prime number varies. These sums are linked to geometrical concepts like the log-canonical threshold, and also to Poisson summation, after the work by Igusa. We will aim to prove a highly generalized form of Igusa's conjecture on exponential sums.'

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