  We continue our study on the corresponding noncommutative deformation of the
relative $p$-adic Hodge structures of Kedlaya-Liu along our previous work. In
this paper, we are going to initiate the study of the corresponding descent of
pseudocoherent modules carrying large noncommutative coefficients. And also we
are going to more systematically study the corresponding noncommutative
geometric aspects of noncommutative deformation of Hodge structures, which will
definitely also provide the insights not only for noncommutative Iwasawa theory
but also for noncommutative analytic geometry. The noncommutative Hodge-Iwasawa
theory is now improved along some very well-defined direction (we will expect
many well-targeted applications to noncommutative Tamagawa number conjectures
from the modern perspectives of Burns-Flach-Fukaya-Kato), while the
corresponding Kedlaya-Liu glueing of pseudocoherent Banach modules with certain
stability is also generalized to the large noncommutative coefficient case.
