3 problems

Let $E/K$ be an elliptic curve with $\operatorname{ord}_{s=1}L(E/K,s)=1$, let $T$ be its $p$-adic Tate module, and let $\vartheta$ be the determinant isomorphism from the Selmer co…

Let $\chi:\operatorname{Gal}(H_{\mathcal C}/K)\to\mathbb C^\times$ be a character, let $\mathfrak s_\chi$ be the associated Stark–Heegner cycle class, and let $L(f/K,\chi,s)$ be th…

Let $f$ be a $p$-new eigenform, let $\mathfrak{p}$ be a prime above $p$, let $V_{\mathfrak{p}}(f)$ be the corresponding $p$-adic representation, let ${\Greekmath 011F}$ be a charac…