Related papers: Invitation to higher local fields, Part I, section…
In this article we study the behavior of inertia groups for modular Galois mod l^n representations and in some cases we give a generalization of Ribet's lowering the level result
We study the behavior of the modular class of a Lie algebroid under general Lie algebroid morphisms by introducing the relative modular class. We investigate the modular classes of pull-back morphisms and of base-preserving morphisms…
Each p-ring class field K(f) modulo a p-admissible conductor f over a quadratic base field K with p-ring class rank r(f) mod f is classified according to Galois cohomology and differential principal factorization type of all members of its…
This work describes several first steps in extending Tate-Iwasawa's analytic method to define an L-function in higher dimensions. For generalizing this method the author advocates the usefulness of the classical Riemann-Hecke approach, his…
One of the key points in Galois theory via field extensions is to build up a correspondence between subfields of a field and subgroups of its automorphism group, so as to study fields via methods of groups. As an analogue of the Galois…
The main result of the paper is a reciprocity law which proves that compatible systems of semisimple, abelian mod $p$ representations (of arbitrary dimension) of absolute Galois groups of number fields, arise from Hecke characters. In the…
We present a unified formulation for higher gauge theory using generalized forms, encompassing higher connections, curvatures, and gauge transformations. We begin by developing the calculus of generalized forms valued in higher algebras and…
We extend the classical duality results of Poitou and Tate for finite discrete Galois modules over local and global fields (local duality, nine-term exact sequence, etc.) to all affine commutative group schemes of finite type, building on…
The purpose of this short note is to fill a gap in the literature: Frobenius reciprocity in the theory of doctrines is closely related to modular connections in projective homological algebra and the notion of a principal element in…
We describe Koszul type complexes associated with a linear map from any module to a free module, and vice versa with a linear map from a free module to an arbitrary module, generalizing the classical Koszul complexes. Given a short complex…
A Galois theory of differential fields with parameters is developed in a manner that generalizes Kolchin's theory. It is shown that all connected differential algebraic groups are Galois groups of some appropriate differential field…
The aim of this article is to generalize Kato's (commutative) p-adic local epsilon-conjecture [Ka93b] for families of (phi,Gamma)-modules over the Robba ring. In particular, we prove the generalized local epsilon-conjecture for rank one…
In this paper, we give a geometrization and a generalization of a lemma of differential Galois theory. This geometrization, in addition of giving a nice insight on this result, offers us the occasion to investigate several points of…
The paper proposes a vector generalization of the basic concepts of the theory of complex variable: the concept of modulus and argument of complex number. The author introduces some generalizations of the notion of holomorphic functions and…
These are lecture notes mainly aimed at graduate students on selected aspects of generalized geometry: in particular generalized complex and Kaehler structures and generalized holomorphic bundles. They are based on lectures given in March…
We examine generalized global symmetries as a kind of compactly supported cohomology, and so are led to revisit questions about the locality of quantum field theory, following Segal. Physics naturally suggests a generalization of…
We propose a generalization of the collective field theory hamiltonian, including interactions between the original bosonic collective field $w_0 (z)$ and supplementary fields ${\bar w}_j (z)$ realizing classically a $w_\infty$ algebra. The…
Enlarging on Parts I, II, and III we write more equations in the desired format of the extended abstract theory of composites. We focus on a multitude of equations involving higher order derivatives. The motivation is that results and…
An algebraic model for the relation between a certain classical particle system and the quantum environment is proposed. The quantum environment is described by the category of possible quantum states. The initial particle system is…
Motivated by obtaining a consistent mathematical description for the radiation reaction of point charged particles in linear classical electrodynamics, a theory of generalized higher order tensors and differential forms is introduced. The…