We consider some nonlocal and nonpolynomial scalar field models originated from p-adic string theory. Infinite number of spacetime derivatives is determined by the operator valued Riemann zeta function through d’Alembertian in its argument. Construction of the corresponding Lagrangians L starts with the exact Lagrangian Lp for effective field of p-adic tachyon string, which is generalized repla...

Let K be a complete discrete valuation field with finite residue field F of order q. We call such a field a local field. The geometric Frobenius FrF is the inverse of the map a 7→ a in the absolute Galois group GF = Gal(F̄ /F ). The Weil group WK is defined as the inverse image of the subgroup 〈FrF 〉 ⊂ GF by the canonical map GK = Gal(K̄/K) → GF . For a scheme XK of finite type over K, the l-adic...

Let p be a fixed odd prime. Throughout this paper Zp, Qp, C, and Cp will, respectively, denote the ring of p-adic rational integers, the field of p-adic rational numbers, the complex number field, and the completion of algebraic closure of Qp. Let vp be the normalized exponential valuation of Cp with |p|p = p −vp(p) = p and let q be regarded as either a complex number q ∈ C or a p-adic number q...

The p-adic description of Higgs mechanism in TGD framework provides excellent predictions for elementary particle and hadrons masses ([email protected] 9410058-62). The gauge group of TGD is just the gauge group of the standard model so that it makes sense to study the p-adic counterpart of the standard model as a candidate for low energy effective theory. Momentum eigen states can be constru...

New approach to p-adic and adelic strings, which takes into account that not only world sheet but also Minkowski space-time and string momenta can be p-adic and adelic, is formulated. p-Adic and adelic string amplitudes are considered within Feynman’s path integral formalism. The adelic Veneziano amplitude is calculated. Some discreteness of string momenta is obtained. Also, adelic coupling con...

The Langlands-Shelstad transfer factor is a function defined on some reductive groups over a p-adic field. Near the origin of the group, it may be viewed as a function on the Lie algebra. For classical groups, its values have the form q sign, where sign ∈ {−1, 0, 1}, q is the cardinality of the residue field, and c is a rational number. The sign function partitions the Lie algebra into three su...

in a commutative noetherian local complex normed algebra which is complete in its m-adic metric there are only finitely many closed prime ideals.

In a previous paper [3], the author gave an explicit description of the algebraic closure of the power series field over a field of characteristic p > 0, in terms of certain “generalized power series”. The purpose of the present paper is to extend this work to mixed characteristic. Specifically, we give an analogous description of the algebraic closure of the Witt ring W (K) of an algebraically...

For a prime number p > 2, we give a direct proof of Breuil’s classification of finite flat group schemes killed by p over the valuation ring of a p-adic field with perfect residue field. As application we establish a correspondence between finite flat group schemes and Faltings’s strict modules which respects associated Galois modules via the Fontaine-Wintenberger field-of-norms functor