Local diophantine properties of Shimura curves

Iwasawa’s Main Conjecture for elliptic curves over anticyclotomic ℤp-extensions

“…(References: see [JoLi1] and [BC] for details, and [BD3,§4] for an exposition.) Assume that M − is strictly greater than 1, and let be a prime dividing M − .…”

“…To obtain the version of the Cerednik-Drinfeld theorem given here, one must descend the isomorphism obtained from the above comparison to Z , using the arguments of Jordan and Livné in [JoLi1]; see also [BC, Ch. III].…”

On the Birch and Swinnerton-Dyer conjecture for modular elliptic curves over totally real fields

“…is the cohomology class defined by τ → w × Id (see [32,Theorem 4.3']). Denote by X 2 the base-change:…”

“…There is an isomorphism of graphs: G h j=1 T /Γ j,+, . The action of Frob on G corresponds under this isomorphism to the action of w (see [32,Section 3]). Then: G h j=1 T /Γ j,+, and the action of Frob on G corresponds to the identity map (see [32,Proposition 3.7]).…”

From the Taniyama-Shimura conjecture to Fermat's last theorem

“…(Further discussion of the mod p reduction of Pic°(C) is found in Kurihara [17], articles of Jordan-Livne [14,15], and [26].) Let The words "naturally isomorphic" are intended to convey the information that the map 03B8 introduced in (6) Next, let us view X Q) X as a T-module via (6).…”