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(0.0) Big Galois representations In this work we study cohomological invariants of “big
Galois representations” ρ: G−→ AutR (T), where (i) G is a suitable Galois group.(ii) R is a …

The topics that we will discuss have their origin in Mazur's synthesis of the theory of elliptic
curves and Iwasawa's theory of Zlp-extensions in the early 1970s. We first recall some …

We prove a general subconvex bound in the level aspect for Rankin–Selberg L-functions
associated with two primitive holomorphic or Maass cusp forms over Q. We use this bound to …

The book surveys some recent developments in the arithmetic of modular elliptic curves. It
places a special emphasis on the construction of rational points on elliptic curves, the Birch …

This article describes a conjectural p-adic analytic construction of global points on (modular)
elliptic curves, points which are defined over the ring class fields of real quadratic fields. The …

We construct the three-variable $ p $-adic triple product $ L $-functions attached to Hida
families of elliptic newforms and prove the explicit interpolation formulae at all critical …

Iwasawa's Main Conjecture for Elliptic Curves over Anticyclotomic Z_p-Extensions
Page 1 Annals of Mathematics, 162 (2005), 1-64 Iwasawa's Main Conjecture for elliptic …

In this paper we solve the subconvexity problem for Rankin-Selberg L-functions where f and
g are two cuspidal automorphic forms over Q, g being fixed and f having large level and …

The purpose of the paper is to extend and refine earlier results of the author on
nonvanishing of the L-functions associated to modular forms in the anticyclotomic tower of …