Related papers: Alg\`ebre absolue

We show that Zilber's conjecture that complex exponentiation is isomorphic to his pseudo-exponentiation follows from the a priori simpler conjecture that they are elementarily equivalent. An analysis of the first-order types in…

Final representation of all those measures $\mu$ for which algebraic polynomials are dense in $L_p(R, d\mu)$ is found. The weighted analogue of the Weierstrass polynomial approximation theorem and a new version of the M. Krein's theorem…

Let $K$ be a totally real number field. For all prime number $p\geq 5$, let us denote by $F_p$ the Fermat curve of equation $x^p+y^p+z^p=0$. Under the assumption that $2$ is totally ramified in $K$, we establish some results about the set…

Let B1 denote the set {0,1} with the usual operations except that $1+1=1$, in other words, the smallest characteristic 1 semifield . We compare two possible analogues of the notion of prime ideal for B1--algebras. We then consider the…

We verify new cases of the Arithmetic Fundamental Lemma (AFL) of Wei Zhang. This relies on a recursive algorithm which allows, under certain conditions, to reduce the AFL identity in question to an AFL identity in lower dimension. The main…

We study the structure of an algebraically closed field with extra function resembling the classical exponentiation on complex numbers.

In this we give a detailed proof of fermionic p-adic q-measures on Z_p and we will treat some interesting formulae related q-extension of Euler numbers and polynomials.

We associate an Albert form to any pair of cyclic algebras of prime degree $p$ over a field $F$ with $\operatorname{char}(F)=p$ which coincides with the classical Albert form when $p=2$. We prove that if every Albert form is isotropic then…

In this paper, for every one-dimensional formal group $F$ we formulate and study a notion of vertex $F$-algebra and a notion of $\phi$-coordinated module for a vertex $F$-algebra where $\phi$ is what we call an associate of $F$. In the case…

Parafermionic conformal field theories are considered on a purely algebraic basis. The generalized Jacobi type identity is presented. Systems of free fermions coupled to each other by nontrivial parafermionic type relations are studied in…

We introduce two-sorted theories in the style of [CN10] for the complexity classes \oplusL and DET, whose complete problems include determinants over Z2 and Z, respectively. We then describe interpretations of Soltys' linear algebra theory…

This paper consists of three parts. In the first part we prove that Zhu's and $C_2$-algebras in type $A$ have the same dimensions. In the second part we compute the graded decomposition of the $C_2$-algebras in type $A$, thus proving the…

Generalizing our earlier work, we introduce the homogeneous quantum $Z$-algebras for all quantum affine algebras $\alg$ of type one. With the new algebras we unite previously scattered realizations of quantum affine algebras in various…

In [ZH], R.B. Zhang found a way to link certain formal deformations of the Lie algebra o(2l+1) and the Lie superalgebra osp(1,2l). The aim of this article is to reformulate the Zhang transformation in the context of the quantum enveloping…

The theory of difference-differential fields of characteristic zero has a model-companion denoted by $\it DCFA$. Previously we proved a weak version of Zilber's dichotomy for $\it DCFA$. In this paper we use arc spaces techniques as…

For a quasilinear $p$-form defined over a field $F$ of characteristic $p>0$, we prove that its defect over the field $F(\sqrt[p^{n_1}]{a_1}, \dots, \sqrt[p^{n_r}]{a_r})$ equals to its defect over the field $F(\sqrt[p]{a_1}, \dots,…

We review some recent results on $K$-theory of perfection of commutative $\mF_p$-algebras and provide an alternative proof.

We propose analogs of the classical Generalized Riemann Hypothesis and the Generalized Simplicity Conjecture for the characteristic p L-series associated to function fields over a finite field. These analogs are based on the use of absolute…

Let $A$ be a unital C$^*$-algebra with unity $1_A$. A pair of elements $0 \le a, b \le 1_A$ in $A$ is said to be \emph{absolutely compatible} if, $\vert a - b \vert + \vert 1_A - a - b \vert = 1_A.$ In this paper we provide a complete…

We state and prove a function field analogue of Furusho for multiple zeta values.