The paper contains a construction of ramification theory for higher dimensional local fields K provided with additional structure given by an increasing sequence of their “subfields of i-dimensional constants”, where 0 i n and n is the dimension of K. It is also announced that a local analogue of the Grothendieck Conjecture still holds: all automorphisms of the absolute Galois group of K, which...

Many problems in computation can be specified in terms of computing the inverseof an easily constructed function. However, studies on how to derive an algorithm froma problem specification involving inverse functions are relatively rare. The aim of thisthesis is to demonstrate, in an example-driven style, a number of techniques to do the job.The techniques are based on the frame...

A bstract We study the manifestly covariant and local 1-loop path integrals on S d +1 for general massive, shift-symmetric (partially) massless totally symmetric tensor fields of arbitrary spin s ≥ 0 in any dimensions 2. After reviewing cases with = 1 , 2, we provide a detailed derivation integer spins 1. Following standard procedure Wick-rotating negative conformal modes, find higher analog Po...

We show that the category of finitely generated free modules over certain local rings is n-angulated for every n ≥ 3. In fact, we construct several classes of nangles, parametrized by equivalence classes of units in the local rings.

Consider now an approach based on a generalization [F2] of Neukirch’s approach [N]. Below is a modified system of axioms of class formations (when applied to topological K -groups) which imposes weaker restrictions than the classical axioms (cf. section 11). (A1). There is a Ẑ-extension of F . In the case of higher local fields let F pur/F be the extension which corresponds to K sep 0 /K0: F pu...

Example. Let X be an algebraic projective irreducible surface over a field k and let P be a closed point of X , C ⊂ X be an irreducible curve such that P ∈ C . If X and C are smooth at P , then we let t ∈ OX,P be a local equation of C at P and u ∈ OX,P be such that u|C ∈ OC,P is a local parameter at P . Denote by C the ideal defining the curve C near P . Now we can introduce a two-dimensional l...