Related papers: Congruences between abelian pseudomeasures

We examine rigidity phenomena for representations of amenable operator algebras which have an ideal of compact operators. We establish that a generalized version of Kadison's conjecture on completely bounded homomorphisms holds for the…

I. M. Milin proposed, in his 1971 paper, a system of inequalities for the logarithmic coefficients of normalized univalent functions on the unit disk of the complex plane. This is known as the Lebedev-Milin conjecture and implies the…

We show that previous correspondence between some (integrable) statistical field theory quantities and periods of $SU(2)$ $\mathcal{N}=2$ deformed gauge theory still holds if we add $N_f=1,2$ flavours of matter. Moreover, the correspondence…

We give a proof of the Morrison--Kawamata cone conjecture for abelian varieties. The proof is a straightforward deduction from well-known results on the real endomorphism algebra of an abelian variety and reduction theory for self-dual…

Braverman and Kahzdan have introduced an influential conjecture on local functional equations for general Langlands $L$-functions. It is related to L. Lafforgue's equally influential conjectural construction of kernels for functorial…

We consider a general reducible gauge theory deformed by mass or/and interaction terms violating gauge invariance. It is shown that in the Abelian case, by using the Stueckelberg-type procedure, this theory with broken gauge symmetry can be…

We present some results from classical homological algebra using the language of cotorsion theories in abelian categories. The results are a couple of foundational facts about homological dimension, the Kunneth formula and the universal…

We discuss abelian equivariant Iwasawa theory for elliptic curves over $\mathbb{Q}$ at good supersingular primes and non-anomalous good ordinary primes. Using Kobayashi's method, we construct equivariant Coleman maps, which send the…

We prove a unicity result for the $L$-functions appearing in the non-commutative Iwasawa main conjecture over totally real fields. We then consider continuous representations $\rho$ of the absolute Galois group of a totally real field $F$…

Let $A$ be an ordinary elliptic curve over a global function field $K$ of characteristic $p$, assumed semistable at every place, and let $L/K$ be a $\mathbb{Z}_p^d$-extension ramified only at finitely many places where $A$ has ordinary…

We obtain direct and inverse approximation theorems of functions of several variables by Taylor-Abel-Poisson means in the integral metrics. We also show that norms of multipliers in the spaces $L_{p,Y}(\mathbb T^d)$ are equivalent for all…

We generalise works of Kobayashi to give a formulation of the Iwasawa main conjecture for modular forms at supersingular primes. In particular, we give analogous definitions of even and odd Coleman maps for normalised new forms of arbitrary…

We establish the exact overlaps conjecture for iterated functions systems on the real line with algebraic contractions and arbitrary translations.

For a given inverse semigroup, one can associate an \'etale groupoid which is called the universal groupoid. Our motivation is studying the relation between inverse semigroups and associated \'etale groupoids. In this paper, we focus on…

Let $\Sigma$ be a strictly convex, compact patch of a $C^2$ hypersurface in $\mathbb{R}^n$, with non-vanishing Gaussian curvature and surface measure $d\sigma$ induced by the Lebesgue measure in $\mathbb{R}^n$. The Mizohata--Takeuchi…

An abstract convergence theorem for a class of generalized descent methods that explicitly models relative errors is proved. The convergence theorem generalizes and unifies several recent abstract convergence theorems. It is applicable to…

We reexamine the notions of generalized Ricci tensor and scalar curvature on a general Courant algebroid, reformulate them using objects natural w.r.t. pull-backs and reductions, and obtain them from the variation of a natural action…

Kato and Fukaya conjectured existence of certain elements in certain ($p$-adic) Iwasawa algebras which are related to Deligne-Langland's ($l$-adic) local epsilon constants. We prove the existence of these elements in the $l \neq p$ case.

We establish a new Iwasawa theory for the kernel of Frobenius on Jacobians of curves in geometric $\mathbf{Z}_p$-towers over the projective line in characteristic $p$, thereby proving several of the main conjectures of [arXiv:2107.12555].

We suggest an extension of the Yang-Mills theory which includes non-Abelian tensor gauge fields. The invariant Lagrangian is quadratic in the field strength tensors and describes interaction of charged tensor gauge bosons of arbitrary large…