Perrin-Riou's Euler system conjecture for $T_\Pi$

Let $T_\Pi$ be the Galois lattice attached to $\Pi$, let $\mathcal O$ be its coefficient ring, and let $\mathcal N$ be the set of integers $mp^k$ where $m$ is a square-free product of integers coprime to the conductor of $T_\Pi$. Put $G_r={\mathrm{Gal}}({\mathbb Q}(\mu_r)/{\mathbb Q})$. Perrin-Riou's Euler system conjecture. There exists a system of cohomological classes

$$\left\{c_r\in\bigwedge^n_{\mathcal O[G_r]}H^1({\mathbb Q}(\mu_r),T_\Pi):r\in\mathcal N\right\}$$

satisfying a precise norm relation as $m$ varies, and the $p$-localization of $c_r$ is related to the complex $L$-values of $T_\Pi^*(1)$ twisted by characters on $G_r$ under the Bloch–Kato dual exponential map. Euler systems are intended to provide global cohomology classes and evidence for Iwasawa main conjectures; the supplied text describes this conjecture as speculative and gives no resolution.