An elliptic eigenform \(f\) of weight \(k\) is said to be \(\theta\)-critical, if it belongs to the image of the \(\theta\)-operator \(\displaystyle \left (\frac{d}{dq}\right )^{k-1}.\) The Iwasawa theory of non-\(\theta\)-critical forms has been extensively studied. In this talk, we are interested in the \(\theta\)-critical case. Using the geometry of the eigencurve and the theory of overconvergent modular symbols, Bellaïche constructed a two-variable \(p\)-adic \(L\)-function in an infinitesimal neighborhood of \(f.\) We give an "étale" construction of this \(p\)-adic \(L\)-function. We also define some Selmer complex which can be seen as the algebraic counterpart of Bellaïche's \(p\)-adic \(L\)-function and discuss the Iwasawa Main Conjecture in this context. This is a joint work with K. Büyükboduk.
Iwasawa theory for critical modular forms
24.05.2022 13:15 - 14:45
Organiser:
H. Grobner, A. Minguez-Espallargas, A. Mellit
Location: