Paraboline variation of $p$-adic families of $(\phi ,\Gamma )$-modules

Abstract

We study the $p$-adic variation of triangulations over $p$-adic families of $(\phi ,\Gamma )$-modules. In particular, we study certain canonical sub-filtrations of the pointwise triangulations and show that they extend to affinoid neighborhoods of crystalline points. This generalizes results of Kedlaya, Pottharst and Xiao and (independently) Liu in the case where one expects the entire triangulation to extend. As an application, we study the ramification of weight parameters over natural $p$-adic families.

46 pages (larger font than before). Final version. Numerous improvements to expositions and corrections of minor errors. Definitions in Section 4 slightly altered following suggestion of referee. Definitions in Sections 5 and 6 explained in more detail for clarity. Appendix added

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