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The purpose of this paper is to build on results in {\it{higher codimensionIwasawa theory}}. The setting of our results involves Galois representationsarising as cyclotomic twist deformations associated to (i) the tensor productof two cuspidal Hida families $F$ and $G$, and (ii) the tensor product of threecuspidal Hida families $F$, $G$ and $H$. On the analytic side, we consider (i)a pair of $3$-variable Rankin-Selberg $p$-adic $L$-functions constructed byHida and (ii) a balanced $4$-variable $p$-adic $L$-function (due to Hsieh andYamana) and an unbalanced $4$-variable $p$-adic $L$-function (whose existenceis currently conjectural). In each of these setups, when the two $p$-adic$L$-functions generate a height two ideal in the corresponding deformationring, we use codimension two cycles of that ring to relate them to a pair ofpseudo-null modules.

Codimension two cycles in Iwasawa theory and tensor product of Hida families