Related papers: Differential Forms, Linked Fields and the $u$-Inva…

Let K be a complete discretely valued field and F the function field of a curve over K. If the characteristic of the residue field k of K is p > 0, then we give a bound for the Brauer p-simension of F in terms of the p-rank of k. If k is a…

Let $\F$ be an algebraically closed field. Let $\V$ be a vector space equipped with a non-degenerate symmetric or symplectic bilinear form $B$ over $\F$. Suppose the characteristic of $\F$ is \emph{large}, i.e. either zero or greater than…

Given a quaternionic form G of a p-adic classical group (p odd) we classify all cuspidal irreducible representations of G with coefficients in an algebraically closed field of characteristic different from p. We prove two theorems: At…

An involution of a real commutative algebra $A$ is a real-linear homomorphism $f : A \rightarrow A$ such that $f^2 = \mathrm{Id}$. We show that there are six involutions of the algebra of bicomplex numbers, contrary to the actual number of…

Let $k$ be a field and suppose $p, q\in k$. We prove that the two affine Hecke algebras $H_q$ and $H_p$ of type $A_n$ are isomorphic as $k$-algebras if and only if $p=q^{\pm 1}$.

For an isotropic reductive group G satisfying a suitable rank condition over an infinite field k, we show that the sections of the $\mathbb{A}^1$-fundamental group sheaf of G over an extension field L/k can be identified with the second…

Let G be a finite abelian group. A number field K is called a Hilbert-Speiser field of type G if for every tame G-Galois extension L/K has a normal integral basis, i.e., the ring of integers O_L is free as an O_K[G]-module. Let C_p denote…

Let $p$ be a prime, $k$ be an algebraically closed field of characteristic $p$. In this paper, we provide the classification of connected Hopf algebras of dimension $p^3$, except the case when the primitive space of the Hopf algebra is two…

We prove that a Hopf algebra of prime dimension $p$ over an algebraically closed field, whose characteristic is equal to $p$, is either a group algebra or a restricted universal enveloping algebra. Moreover, we show that any Hopf algebra of…

We examine the following fourth order H\'enon equation \label{pipe} \Delta^2 u = |x|^\alpha u^p \qquad \text{in}\ \IR^N, where $ 0 < \alpha$. Define the Hardy-Sobolev exponent $ p_4(\alpha):= \frac{N+4 + 2 \alpha}{N-4}$. We show that in…

We study a pair of Calabi-Yau threefolds X and M, fibered in non-principally polarized Abelian surfaces and their duals, and an equivalence D^b(X) = D^b(M), building on work of Gross, Popescu, Bak, and Schnell. Over the complex numbers, X…

In this paper we obtain an asymptotic formula for the number of $\operatorname{SL}_2(\mathbb{Z})$-equivalence classes of positive definite binary quadratic forms over $\bZ$ having bounded discriminant $\Delta = 1-4p$, with $p$ a prime. We…

Oleg Viro studied in arXiv:math/0204290 two interpretations of the (multivariable) Alexander polynomial as a quantum link invariant: either by considering the quasi triangular Hopf algebra associated to $U_q sl(2)$ at fourth roots of unity,…

Construction of a universal finite-type invariant can be reduced, under suitable assumptions, to the solution of certain equations (the hexagon and pentagon equations) in a particular graded associative algebra of chord diagrams. An…

Let E/F be a quadratic number (resp. p-adic) field extension, and F' an odd degree cyclic field extension of F. We establish a base-change functorial lifting of automorphic (resp. admissible) representations from the unitary group U(3,E/F)…

Let $\pi$ be a cuspidal, cohomological automorphic representation of an inner form $G$ of $\mathrm{PGL}_2$ over a number field $F$ of arbitrary signature. Further, let $\mathfrak{p}$ be a prime of $F$ such that $G$ is split at…

The problem of extending derivations of a field $F$ to an $F-$algebra $B$ is widely studied in commutative algebra and non-commutative ring theory. For example, every derivation of $F$ extends to $B$ if $B$ is a separable algebraic…

A graph is \emph{$(\mathcal{I}, \mathcal{F})$-partitionable} if its vertex set can be partitioned into two parts such that one part $\mathcal{I}$ is an independent set, and the other $\mathcal{F}$ induces a forest. A graph is…

We define and compute $\operatorname{ABrd}_p(F)$, the asymptotic Brauer $p$-dimension of a field $F$, in cases where $F$ is a rational function field or Laurent series field. $\operatorname{ABrd}_p(F)$ is defined like the Brauer…

Real Heegaard Floer homology is an invariant associated to a three-manifold equipped with an involution with nonempty fixed set of codimension two. We show that when the image of the fixed point set is nullhomologous in the quotient, the…