Explore the words cloud of the CriticalGZ project. It provides you a very rough idea of what is the project "CriticalGZ" about.
The following table provides information about the project.
UNIVERSITY COLLEGE DUBLIN, NATIONAL UNIVERSITY OF IRELAND, DUBLIN
|Coordinator Country||Ireland [IE]|
|Total cost||152˙988 €|
|EC max contribution||152˙988 € (100%)|
1. H2020-EU.1.3.2. (Nurturing excellence by means of cross-border and cross-sector mobility)
|Duration (year-month-day)||from 2017-08-01 to 2019-07-31|
Take a look of project's partnership.
|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|
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.
|year||authors and title||journal||last update|
KÃ¢zÄ±m BÃ¼yÃ¼kboduk, 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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