Relational Iwasawa Theory and the arithmetic of conjugate-symplectic motives

This project has two goals, in the context of the study of the relations among algebraic cycles, Selmer groups, and p-adic L-functions. The first goal is to prove many more cases of the p-adic Beilinson-Bloch-Kato conjecture for higher rank motives (characterised by a conjugate-symplectic symmetry). The second goal is to chart an adequate and up-to-date conjectural framework (Relational Iwasawa theory) describing the precise relations among p-adic L-functions and Selmer groups, and to collect old and new evidence for it.