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We investigate properties of the Euler system associated to certainautomorphic representations of the unitary similitude group GU(2,1) withrespect to an imaginary quadratic field $E$, constructed byLoeffler-Skinner-Zerbes. By adapting Mazur and Rubin's Euler system machinerywe prove one divisibility of the ``rank 1" Iwasawa main conjecture under somemild hypotheses. When $p$ is split in $E$ we also prove a ``rank 0" statementof the main conjecture, bounding a particular Selmer group in terms of a$p$-adic distribution conjecturally interpolating complex $L$-values. We thenprove descended versions of these results, at integral level, where we boundcertain Bloch--Kato Selmer groups. We will also discuss the case where $p$ isinert, which is a work in progress.

Euler Systems and Selmer Bounds for GU(2,1)