Abstract In a paper published in 1980, the author gave an adelic Tamagawa number interpretation for Birch and Swinnerton-Dyer conjecture divisors on abelian varieties. Some years later, joint work with K. Kato, more general volume zeta values of motives weights $${<}\,{-1}$$ was proposed. at hand, is generalized to deal weight $$-1$$ . As points varieties are replaced by cohomology coefficie...

In this paper, we introduce pyramid-adapted shearlet systems for the three-dimensional setting, and show how one can construct frames for L(R) with this particular shearlet structure. We then introduce a generalized three-dimensional cartoon-like image model class of piecewise C smooth functions with discontinuities on a C smooth surface with 1 < α ≤ 2 and show that pyramid-adapted shearlet sys...

The mathematical basis of p-adic Higgs mechanism discussed in papers [email protected] 9410058-62 is considered in this paper. The basic properties of p-adic numbers, of their algebraic extensions and the so called canonical identification between positive real numbers and p-adic numbers are described. Canonical identification induces p-adic topology and differentiable structure on real axis ...

In this paper a countable family of new compactly supported non-Haar p-adic wavelet bases in L(Q p ) is constructed. We use the wavelet bases in the following applications: in the theory of p-adic pseudo-differential operators and equations. Namely, we study the connections between wavelet analysis and spectral analysis of p-adic pseudo-differential operators. A criterion for a multidimensional...

The notion of a p-adic superspace is introduced and used to give a transparent construction of the Frobenius map on p-adic cohomology of a smooth projective variety over Z p (the ring of p-adic integers). This article partially intersects with [9]; it contains the proofs omitted in [9] as well as some investigations into the important notion of a prorepresentable p-adic superspace.

The specializations of the motivic elliptic polylogarithm on the universal elliptic curve to the modular curve are referred to as Eisenstein classes. In this paper, we prove that the syntomic realization of the Eisenstein classes restricted to the ordinary locus of the modular curve may be expressed using p-adic Eisenstein series of negative weight, which are p-adic modular forms defined using ...