The aim of this paper is to prove the weight-monodromy conjecture (Deligne’s conjecture on the purity of monodromy filtration) for varieties with p-adic uniformization 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 an argument of Steenbrink, M. Saito to the weight spectral sequence of Rapop...

The aim of this paper is to study certain properties of the weight spectral sequences of Rapoport-Zink by a specialization argument. By reducing to the case over finite fields previously treated by Deligne, we prove that the weight filtration and the monodromy filtration defined on the l-adic étale cohomology coincide, up to shift, for proper smooth varieties over equal characteristic local fie...

Towers of function fields (resp., of algebraic curves) with positive limit provide examples of curves with large genus having many rational points over a finite field. It is in general a difficult task to calculate the genus of a wild tower. In this paper, we present a method for calculating the genus of certain Artin–Schreier towers. As an illustration of our method, we obtain a very simple an...

We combine Lurie’s generalization of the Hopkins–Miller theorem with work of Zink–Lau on displays to give a functorial construction of even-periodic E1 ring spectra E , concentrated in chromatic layers 2 and above, associated to certain n n invertible matrices with coefficients in the Witt ring of 0.E/ . This is applied to examples related to Lubin–Tate and Johnson–Wilson spectra. We also give ...

In this paper, we study special cycles on the Krämer model of $$\mathrm {U}(1,1)(F/F_0)$$ -Rapoport–Zink spaces where $$F/F_0$$ is a ramified quadratic extension p-adic number fields with assumption that 2-dimensional hermitian space quasi-homomorphisms anisotropic. We write down decomposition these and prove version Kudla–Rapoport conjecture in case. then apply local results to compute interse...

We formulate and prove a local arithmetic Siegel–Weil formula for GSpin Rapoport–Zink spaces, which is precise identity between the intersection numbers of special cycles on spaces derivatives representation densities quadratic forms. As first application, we semi-global as conjectured by Kudla, relates Shimura varieties at place good reduction central nonsingular Fourier coefficients incoheren...