Cel 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. Dziedzina nauki natural sciencesmathematicspure mathematicsarithmeticslogarithmic functions Program(-y) H2020-EU.1.3. - EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions Main Programme H2020-EU.1.3.2. - Nurturing excellence by means of cross-border and cross-sector mobility Temat(-y) MSCA-IF-2016 - Individual Fellowships Zaproszenie do składania wniosków H2020-MSCA-IF-2016 Zobacz inne projekty w ramach tego zaproszenia System finansowania MSCA-IF-GF - Global Fellowships Koordynator UNIVERSITY COLLEGE DUBLIN, NATIONAL UNIVERSITY OF IRELAND, DUBLIN Wkład UE netto € 152 988,00 Adres BELFIELD 4 Dublin Irlandia Zobacz na mapie Region Ireland Eastern and Midland Dublin Rodzaj działalności Higher or Secondary Education Establishments Linki Kontakt z organizacją Opens in new window Strona internetowa Opens in new window Uczestnictwo w unijnych programach w zakresie badań i innowacji Opens in new window sieć współpracy HORIZON Opens in new window Koszt całkowity € 152 988,04 Uczestnicy (1) Sortuj alfabetycznie Sortuj według wkładu UE netto Rozwiń wszystko Zwiń wszystko KOC UNIVERSITY Zakończenie uczestnictwa Turcja Wkład UE netto € 0,00 Adres RUMELI FENERI YOLU SARIYER 34450 Istanbul Zobacz na mapie Region İstanbul İstanbul İstanbul Rodzaj działalności Higher or Secondary Education Establishments Linki Kontakt z organizacją Opens in new window Strona internetowa Opens in new window Uczestnictwo w unijnych programach w zakresie badań i innowacji Opens in new window sieć współpracy HORIZON Opens in new window Koszt całkowity Brak danych Partnerzy (1) Sortuj alfabetycznie Sortuj według wkładu UE netto Rozwiń wszystko Zwiń wszystko Partner Organizacje partnerskie biorą udział w realizacji działania, jednak nie podpisują umowy o grant. PRESIDENT AND FELLOWS OF HARVARD COLLEGE Stany Zjednoczone Wkład UE netto € 0,00 Adres MASSACHUSETTS AVENUE 1350 02138 Cambridge Zobacz na mapie Rodzaj działalności Higher or Secondary Education Establishments Linki Kontakt z organizacją Opens in new window Strona internetowa Opens in new window Uczestnictwo w unijnych programach w zakresie badań i innowacji Opens in new window sieć współpracy HORIZON Opens in new window Koszt całkowity € 80 065,20
