We give an example of a projective smooth surface X over a p-adic field K such that for any prime l different from p, the l-primary torsion subgroup of CH0(X), the Chow group of 0-cycles on X, is infinite. A key step in the proof is disproving a variant of the Block-Kato conjecture which characterizes the image of an l-adic regulator map from a higher Chow group to a continuous étale cohomology...

The only quadrature operator of order two on L2(R) which covaries with orthogonal transforms, in particular rotations is (up to the sign) the Riesz transform. This property was used for the construction of monogenic wavelets and curvelets. Recently, shearlets were applied for various signal processing tasks. Unfortunately, the Riesz transform does not correspond with the shear operation. In thi...

We propose an algorithmic framework based on ADMM/split Bregman that combines a multilevel adapted, iterative reweighting strategy and a second total generalized variation regularizer. The level adapted reweighting strategy is a combination of reweighted `-minimization and additional compensation factors for a uniform treatment of the sparsity structure across all levels. Classical multilscale ...

It is shown that the p-adic Banach spaces introduced by Emerton, are isomorphic to the cohomology groups of the sheaf of continuous Qp-valued functions on a certain space. Some applications of this result are discussed.

We classify the irreducible, admissible, smooth, genuine mod p representations of the metaplectic double cover of SL2(F ), where F is a p-adic field and p 6= 2. We show, using a generalized Satake transform, that each such representation is isomorphic to a certain explicit quotient of a compact induction from a maximal compact subgroup by an action of a spherical Hecke operator, and we define a...

Using the Weyl quantization we formulate one-dimensional adelic quantum mechanics, which unifies and treats ordinary and p-adic quantum mechanics on an equal footing. As an illustration the corresponding harmonic oscillator is considered. It is a simple, exact and instructive adelic model. Eigenstates are Schwartz-Bruhat functions. The Mellin transform of a simplest vacuum state leads to the we...

This is a foundational account of the étale topology of generalized Witt vectors and of related constructions. The theory of the usual, “p-typical” Witt vectors of p-adic schemes of finite type is already reasonably well developed. The main point here is to generalize this theory in two different ways. We allow not just p-typical Witt vectors but also, for example, those taken with respect to a...