Resumen de The V-filtration for tame unit FF-crystals

Theodore J. Stadnik

• Let XX be a smooth variety over an algebraically closed field of characteristic p>0,Zp>0,Z a smooth divisor, and j:U=X∖Z→Xj:U=X∖Z→X the natural inclusion. We introduce in an axiomatic way the notion of a VV -filtration on unit FF -crystals and prove such axioms determine a unique filtration. It is shown that if MM is a tame unit FF -crystal on UU , then such a VV -filtration along ZZ exists on j∗Mj∗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 A1A1 and gluing are then discussed.