Monodromy Filtration and Positivity
نویسندگان
چکیده
We study Deligne’s conjecture on the monodromy weight filtration on the nearby cycles in the mixed characteristic case, and reduce it to the nondegeneracy of certain pairings in the semistable case. We also prove a related conjecture of Rapoport and Zink which uses only the image of the Cech restriction morphism, if Deligne’s conjecture holds for a general hyperplane section. In general we show that Deligne’s conjecture is true if the standard conjectures hold.
منابع مشابه
Weight-monodromy Conjecture for Certain Threefolds in Mixed Characteristic
The weight-monodromy conjecture claims the coincidence of the shifted weight filtration and the monodromy filtration on étale cohomology of a proper smooth variety over a complete discrete valuation field. Although it was already proved in some cases, the case of dimension ≥ 3 in mixed characteristic is still unproved up to now. The aim of this paper is to prove the weight-monodromy conjecture ...
متن کاملVanishing cycle sheaves of one-parameter smoothings
We study the vanishing cycles of a one-parameter smoothing of a complex analytic space and show that the weight filtration on its perverse cohomology sheaf of the highest degree is quite close to the monodromy filtration so that its graded pieces have a modified Lefschetz decomposition. We also describe its primitive part using the weight filtration on the perverse cohomology sheaves of the con...
متن کاملSingularities of Variations of Mixed Hodge Structure
We prove that a variation of graded-polarizable mixed Hodge structure over a punctured disk with unipotent monodromy, has a limiting mixed Hodge structure at the puncture (i.e., it is admissible in the sense of [SZ]) which splits over R, if and only if certain grading of the complexified weight filtration, depending smoothly on the Hodge filtration, has a real limit at the puncture. In particul...
متن کاملLocal monodromy of p-adic differential equations: an overview
This primarily expository article collects together some facts from the literature about the monodromy of differential equations on a p-adic (rigid analytic) annulus, though often with simpler proofs. These include Matsuda’s classification of quasiunipotent ∇-modules, the Christol-Mebkhout construction of the ramification filtration, and the Christol-Dwork Frobenius antecedent theorem. We also ...
متن کاملMaximal wild monodromy in unequal characteristic
Let R be a complete discrete valuation ring of mixed characteristic (0, p) with fraction field K. We study stable models of p-cyclic covers of PK . First, we determine the monodromy extension, the monodromy group, its filtration and the Swan conductor for special covers of arbitrarily high genus with potential good reduction. In the case p = 2 we consider hyperelliptic curves of genus 2.
متن کامل