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arXiv · 1410.3412

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

John Bergdall
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Abstract

We study the $p$-adic variation of triangulations over $p$-adic families of $(\varphi,\Gamma)$-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.

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John Bergdall. 2014-10-13. Paraboline variation of $p$-adic families of $(\varphi,\Gamma)$-modules. https://doi.org/10.1112/s0010437x16007831

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