Weight-monodromy conjecture for p-adically uniformized varieties

By Tetsushi Ito. 2003

69 citations recorded by the source corpus.

The aim of this paper is to prove the weight-monodromy conjecture (Deligne’s conjecture on the purity of monodromy filtration) for varieties p-adically uniformized by the Drinfeld upper half spaces of any dimension. The ingredients of the proof are to prove a special case of the Hodge standard conjecture, and apply a positivity argument of Steenbrink, M. Saito to the weight spectral sequence of Rapoport-Zink. As an application, by combining our results with the results of Schneider-Stuhler, we compute the local zeta functions of p-adically uniformized varieties in terms of representation theoretic invariants. We also consider a p-adic analogue by using the weight spectral sequence of Mokrane.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/68a7356cc0d348023928ac8d2c1d0e788859e2c2

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Citations in the corpus

Perfectoid Spaces (2011, background): “Notably, the case of varieties which admit p-adic uniformization by Drinfeld’s upper half-space is proved by Ito, [25], by pushing through the argument of Rapoport-Zink in this special case, making use of the special nature of the components of the special fibre, which are explicit rational varietie”
On non-abelian Lubin-Tate theory via vanishing cycles (2004, methodology): “licity is qn−h −1. The inverse image YP,st of YP in Zst is the unique proper component of the special ﬁber of Zst, whose multiplicity is qn −1. This YP,st is isomorphic to the Bn−1 in the notation of [It], Section 4, and Y N,st ∩YP,st is isomorphic to Bh ×Bn−h−2. Note that all the blow-upsperformedh”
Hilbert modular forms and the Ramanujan conjecture (2005, background): “to refer to the l-adic intersection cohomologies of the Baily-Borel compactiﬁcation of ShB,W. 3. Several authors have recently made signiﬁcant progress on cases of WMC involving Shimura varieties. In [It2], instances of WMC are shown for certain Shimura varieties Shassociated to unitary groups. In f”
Théorie de Lubin-Tate non-abélienne et représentations elliptiques (2006, unknown): “Signalons brièvement qu’outre les courbes et les variétés abéliennes traitées dans SGA 7, la conjecture monodromie-poids est connue pour les surfaces semi-stables [43], les variétés uniformisées par Ωd−1 K [38] [17], et les variétés de Shimura de type Harris-Taylor grâce à Boyer [12, Thm 14.”