The V-filtration for tame unit F-crystals |
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Authors: | Theodore J Stadnik Jr |
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Institution: | 1. Northwestern University, Evanston, IL, USA
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Abstract: | Let \(X\) be a smooth variety over an algebraically closed field of characteristic \(p > 0, Z\) a smooth divisor, and \(j: U=X {\setminus } Z \rightarrow X\) the natural inclusion. We introduce in an axiomatic way the notion of a \(V\) -filtration on unit \(F\) -crystals and prove such axioms determine a unique filtration. It is shown that if \(\mathcal M \) is a tame unit \(F\) -crystal on \(U\) , then such a \(V\) -filtration along \(Z\) exists on \(j_*\mathcal M \) . The degree zero component of the associated graded module is proven to be the (unipotent) nearby cycles functor of Grothendieck and Deligne under the Emerton–Kisin Riemann–Hilbert correspondence. A few applications to \(\mathbb A ^1\) and gluing are then discussed. |
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