The Bloch–Kato conjecture for critical premotivic structures

Let $M$ be a critical object of $\operatorname{{\bf PM}}_K$, let $b(M)$ be the basis supplied by Deligne's period conjecture, let $\lambda$ be a place of $K$ for which the stated vanishing condition holds, and let $\delta_{f,\lambda}(M)$ be the fractional ideal defined from the relevant Fitting ideals and Tamagawa factors. Bloch–Kato conjecture.

$$\delta_{f,\lambda}(M)=(1\otimes b(M))\mathcal{O}_\lambda.$$

This is the $\lambda$-part of the Bloch–Kato conjecture, relating special values and periods to Selmer-theoretic arithmetic invariants. The paper proves the relevant result for the modular-form cases under its hypotheses, but the displayed formulation is presented as a general conjecture.