On the Galois structure of arithmetic cohomology, III: Selmer groups of critical motives

Abstract

We investigate the explicit Galois structures of Bloch–Kato Selmer groups of $p$-adic realizations of critical motives. We show in particular that, under natural and relatively mild hypotheses, the Krull–Schmidt decompositions of the $p$-adic lattices arising from such Selmer groups are dominated by very simple indecomposable modules (even when the ranks are very large).