IWASAWA THEORY FOR SYMMETRIC SQUARES OF NON-p-ORDINARY EIGENFORMS

期刊： DOCUMENTA MATHEMATICA, 2021; 26 ()

Let f be a normalized cuspidal eigen-newform of level coprime to p with a(p)(f) = 0. We formulate both integral signed Iwasawa main conjectures and an......

HECKE L-FUNCTIONS AND FOURIER COEFFICIENTS OF COVERING EISENSTEIN SERIES

期刊： DOCUMENTA MATHEMATICA, 2021; 26 ()

We consider in this paper covering groups and Fourier coefficients of Eisenstein series for induced representations from certain distinguished theta r......

GENERIC SMOOTH REPRESENTATIONS

期刊： DOCUMENTA MATHEMATICA, 2020; 25 ()

Let F be a non-archimedean local field. In this paper we explore genericity of irreducible smooth representations of GL(n) (F) by restriction to a max......

ON THE CONTROL THEOREM FOR FINE SELMER GROUPS AND THE GROWTH OF FINE TATE-SHAFAREVICH GROUPS IN Z(p)-EXTENSIONS

期刊： DOCUMENTA MATHEMATICA, 2020; 25 ()

Let A be an abelian variety defined over a number field F. We prove a control theorem for the fine Selmer group of the abelian variety A which essenti......

A CLASSICAL FAMILY OF ELLIPTIC CURVES HAVING RANK ONE AND THE 2-PRIMARY PART OF THEIR TATE-SHAFAREVICH GROUP NON-TRIVIAL

期刊： DOCUMENTA MATHEMATICA, 2020; 25 ()

We study elliptic curves of the form x(3) + y(3) = 2p and x(3) + y(3) = 2p(2) where p is any odd prime satisfying p equivalent to 2 mod 9 or p equival......