Related papers: Fesenko reciprocity map

We prove that arboreal Galois extensions of number fields are never abelian for post-critically finite rational maps and non-preperiodic base points. For polynomials, this establishes a new class of known cases of a conjecture of…

The article is a contribution to the local theory of geometric Langlands correspondence. The main result is a categorification of the isomorphism between the (extended) affine Hecke algebra, thought of as an algebra of Iwahori bi-invariant…

For a quasi-projective scheme $X$ admitting a smooth compactification over a local field of residue characteristic $p > 0$, we construct a continuous reciprocity homomorphism from a tame class group to the abelian tame etale fundamental…

We define a motivic conductor for any presheaf with transfers $F$ using the categorical framework developed for the theory of motives with modulus by Kahn-Miyazaki-Saito-Yamazaki. If $F$ is a reciprocity sheaf this conductor yields an…

We sketch the construction of a derived enhancement of the reciprocity isomorphism of class field theory. Details will appear in a forthcoming joint paper of the authors with A. Raksit.

Author's generalization of one-dimensional class field theory to theory of abelian totally ramified p-extensions of a complete discrete valuation field with arbitrary non-separably p-closed residue field and its applications are described.

Neukirch developed an axiomatic and explicit approach to class field theory. This was applied to local fields and number fields but was never done for global function fields since he believed that geometric approach is more suitable.…

This paper establishes a relationship between finite extensions and norm groups of formally real quasilocal fields, which yields a generally nonabelian local class field theory, including analogues to the fundamental correspondence, the…

The paper establishes a relationship between finite separable extensions and norm groups of strictly quasilocal fields with Henselian discrete valuations, which yields a generally nonabelian one-dimensional local class field theory.

We present elements of a theory of translation-invariant integration on finite dimensional vector spaces and on GL_n over a valuation field with local field as residue field. We then discuss the case of an arbitrary algebraic group. This…

Koya's and author's approach to the higher local reciprocity map as a generalization of the classical class formations approach to the level of complexes of Galois modules.

In this expository paper we provide a geometric proof of the local Langlands Correspondence for the groups $\operatorname{GL}_{1}$ defined over $p$-adic fields $K$. We do this by redeveloping the theory of proalgebraic groups and use this…

We construct analogues of Rankin--Selberg integrals for Speh representations of the general linear group over a $p$-adic field. The integrals are in terms of the Shalika model and are expected to be the local counterparts of (suitably…

Let $L/K$ be a finite Galois extension of local fields. The Hasse-Arf theorem says that if Gal$(L/K)$ is abelian then the upper ramification breaks of $L/K$ must be integers. We prove the following converse to the Hasse-Arf theorem: Let $G$…

We give a new geometric characterization of the motivic ramification filtration of reciprocity sheaves, by imitating a method used by Abbes and (Takeshi) Saito to study the ramification of torsors under finite \'etale groups. This new…

We study the relationship between the local and global Galois theory of function fields over a complete discretely valued field. We give necessary and sufficient conditions for local separable extensions to descend to global extensions, and…

K. Kato's conjecture about the cohomological Hasse principle for regular connected schemes $\mathfrak X$ which are flat and proper over the complete discrete valuation rings $\mathcal O_N$ of higher local fields $F_N$ is proven. This…

In this paper, we prove the $\ell$-adic abelian class field theory for henselian regular local rings of equi-characteristic assuming the surjectivity of Galois symbol maps, which is a $\ell$-adic variant of a result of Matsumi [13].

In this paper, using what we call a micro reciprocity law, we complete Weil's program for non-abelian class field theory of Riemann surfaces.

Neukirch has developed explicit and axiomatic class field theory, which applies to both local and global fields. One of the key ingredients in his theory is a $\hat{\mathbb{Z}}$-extension of the base field, and in the case of…