Related papers: Explicit reciprocity laws for higher local fields

For primes p greater than 3, we propose a conjecture that relates the values of cup products in the Galois cohomology of the maximal unramified outside p extension of a cyclotomic field on cyclotomic p-units to the values of p-adic…

We draw concrete consequences from our arithmetic duality for two-dimensional local rings with perfect residue field. These consequences include class field theory, Hasse principles for coverings and $K_{2}$ and a duality between divisor…

In a previous paper of the author, we establish a duality for the direct limit and the inverse limit of higher even $K$-groups over a $\mathbb{Z}_p^d$-extension. In this paper, we shall establish such a duality over certain non-commutative…

We establish precise relations between Euler systems that are respectively associated to a $p$-adic representation $T$ and to its Kummer dual $T^*(1)$. Upon appropriate specialization of this general result, we are able to deduce the…

We study graduated orders over completed group rings of $1$-dimensional admissible $p$-adic Lie groups, and verify the equivariant $p$-adic Artin conjecture for such orders. Following Jacobinski and Plesken, we obtain a formula for the…

We prove a version of the Gindikin-Karpelevich formula for untwisted affine Kac-Moody groups over a local field of positive characteristic. The proof is geometric and it is based on the results of [1] about intersection cohomology of…

We identify the dominant part of the Frenkel-Reshetikhin $q$-character with a natural invariant arising from the Langlands/Zelevinsky parameterization for affine Hecke algebras. We introduce the reciprocal character of a module over a…

The classification of the local Galois representations using $(\varphi,\Gamma)$-modules by Fontaine has been generalized by Kisin and Ren over the Lubin-Tate extensions of local fields using the theory of $(\varphi_q,\Gamma_{LT})$-modules.…

Affine Hecke algebras arise naturally in the study of smooth representations of reductive $p$-adic groups. Finite dimensional complex representations of affine Hecke algebras (under some restriction on the isogeny class and the parameter…

We give explicit, uniform formulas for the graded characters and total ranks of the Lie algebra homology of finite-dimensional representations in all classical types. In many cases, these compute the Tor groups of finite length modules over…

The construction of the $p$-adic local Langlands correspondence for $\mathrm{GL}_2(\mathbf{Q}_p)$ uses in an essential way Fontaine's theory of cyclotomic $(\varphi,\Gamma)$-modules. Here \emph{cyclotomic} means that $\Gamma =…

the program of Langlands is studied here on the basis of: a)new concepts of global class field theory related to the explicit construction of global class fields and of reciprocity laws; b)the representations of the reductive algebraic…

Generalized dualities had an intriguing incursion into Double Field Theory (DFT) in terms of local $O(d,d)$ transformations. We review this idea and use the higher derivative formulation of DFT to compute the first order corrections to…

The classical Artin--Whaples approximation theorem allows to simultaneously approximate finitely many different elements of a field with respect to finitely many pairwise inequivalent absolute values. Several variants and generalizations…

We compute the Grothendieck group of certain 2-Calabi--Yau triangulated categories appearing naturally in the study of the link between quiver representations and Fomin--Zelevinsky's cluster algebras. In this setup, we also prove a…

We extend Kato explicit reciprocity law, in the version written by Scholl, for a modular curve to a product of two modular curves. By embedding the product of two modular curves in the Siegel threefold, we deduce an explicit reciprocity law…

We use the properties of Hermite and Kamp\'e de F\'eriet polynomials to get closed forms for the repeated derivatives of functions whose argument is a quadratic or higher-order polynomial. The results we obtain are extended to product of…

We apply the super duality formalism recently developed by the authors to obtain new equivalences of various module categories of general linear Lie superalgebras. We establish the correspondence of standard, tilting, and simple modules, as…

We give a new formula for the special value at s=2 of the Hasse-Weil zeta function for smooth projective fourfolds under some assumptions (the Tate and Beilinson conjecture, finiteness of some cohomology groups, etc.). Our formula may be…

We introduce cosurfaces with values in the group \(\PC_n(H)\) of \(H\)-valued reciprocal pairwise comparison matrices. The composition law is covariant on upper triangular coefficients and contravariant on lower triangular coefficients,…