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CriticalGZ SIGNED

Critical Slope Gross-Zagier formula and Perrin-Riou's Conjecture

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EC-Contrib. €

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Partnership

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Project "CriticalGZ" data sheet

The following table provides information about the project.

Coordinator
UNIVERSITY COLLEGE DUBLIN, NATIONAL UNIVERSITY OF IRELAND, DUBLIN 

Organization address
address: BELFIELD
city: DUBLIN
postcode: 4
website: www.ucd.ie

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country Ireland [IE]
 Project website https://maths.ucd.ie/
 Total cost 152˙988 €
 EC max contribution 152˙988 € (100%)
 Programme 1. H2020-EU.1.3.2. (Nurturing excellence by means of cross-border and cross-sector mobility)
 Code Call H2020-MSCA-IF-2016
 Funding Scheme MSCA-IF-GF
 Starting year 2017
 Duration (year-month-day) from 2017-08-01   to  2019-07-31

 Partnership

Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    UNIVERSITY COLLEGE DUBLIN, NATIONAL UNIVERSITY OF IRELAND, DUBLIN IE (DUBLIN) coordinator 152˙988.00
2    KOC UNIVERSITY TR (ISTANBUL) participant 0.00
3    PRESIDENT AND FELLOWS OF HARVARD COLLEGE US (CAMBRIDGE) partner 0.00

Map

 Project objective

The main objective of this project is to prove a p-adic Gross-Zagier formula for the critical slope p-adic L-functions attached to p-ordinary modular forms. As we will explain in the main body of this proposal, such a formula will lead, among other things, to a full proof of a conjecture of Perrin-Riou (that gives a precise comparison between p-adic Beilinson-Kato elements and Heegner points).

Our approach will rely heavily on the theme of p-adic variation and will consist of three major steps (which, we believe, are independent on their own right):

As the first step, we would like to interpolate the Heegner cycles associated to modular forms along Coleman families. This has been carried out for p-ordinary forms by Benjamin Howard (and complemented by the work of Francesc Castella, befitting our goals).

The second step is to carry out a construction of the two-variable p-adic L-function for the base change of a Coleman family (over an affinoid A, say) to the suitable imaginary quadratic field. We note here that such a p-adic L-function over the field of rationals has been constructed by Joel Bellaiche.

The third and final step is to prove p-adic Gross-Zagier formulae for individual (p-non-ordinary) members of the family. This has been carried out by S. Kobayashi for weight 2 forms; we aim to provide a generalisation of his work to higher weights.

Noting that p-adic height pairings readily deform well in families (thanks to the work of Denis Benois, in this context), we aim to prove a A-adic Gross-Zagier formula for the cyclotomic derivative of the base change p-adic L-function. This formula, when specialized to weight 2, will yield the desired formula.

In the duration of this fellowship, we also intend to carry out several projects with our long-term collaborator Antonio Lei. We shall provide a brief account for these in the main body of our proposal.

 Publications

year authors and title journal last update
List of publications.
2019 Kâzım Büyükboduk, Antonio Lei
Rank-two Euler systems for symmetric squares
published pages: 1, ISSN: 0002-9947, DOI: 10.1090/tran/7860
Transactions of the American Mathematical Society 2019-08-29

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The information about "CRITICALGZ" are provided by the European Opendata Portal: CORDIS opendata.

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