Zeta elements for $p$-ordinary modular forms over imaginary quadratic fields and applications

Let $p\geq 5$ be a prime, and let $f$ be a $p$-ordinary cuspidal newform of even weight $k = 2r \geq 2$ and level $N$, with $p \nmid N$ and trivial nebentype. In this article, we prove Kato's Iwasawa main conjecture for $f$, formulated in terms of the $p$-adic $L$-function of $f$, under the sole ass