Iwasawa cohomology of pseudorigid families of $(\phi ,\mathrm{\Gamma })$-modules

We study the Iwasawa cohomology complex attached to a pseudorigid family of $(\phi ,\mathrm{\Gamma })$-modules and prove coadmissibility of its cohomology groups, perfectness and compatibility with base change. We apply this result to give another proof of perfectness of the Herr complex in pseudorigid family. We also use it to prove perfectness of Selmer complexes and obtain a result on variation of ranks of Selmer groups in analytic family.