相关论文: On Brauer $p$-dimensions and absolute Brauer $p$-d…

Let $(K, v)$ be a Henselian discrete valued field with residue field $\widehat K$ of characteristic $p$, and Brd$_{p}(K)$ be the Brauer $p$-dimension of $K$. This paper shows that Brd$_{p}(K) \ge n$, if $[\widehat K\colon \widehat K ^{p}] =…

Let $(K, v)$ be a Henselian discrete valued field with residue field $\widehat K$ of characteristic $q \ge 0$, and Brd$_{p}(K)$ be the Brauer $p$-dimension of $K$, for each prime $p$. The present paper shows that if $p = q$, then…

The present paper shows that if $q \in \mathbb P$ or $q = 0$, where $\mathbb P$ is the set of prime numbers, then there exist characteristic $q$ fields $E _{q,k}\colon \ k \in \mathbb N$, of Brauer dimension Brd$(E _{q,k}) = k$ and infinite…

Let $(K, v)$ be a Henselian discrete valued field with a quasifinite residue field. This paper proves the existence of an algebraic extension $E/K$ satisfying the following: (i) $E$ has dimension dim$(E) \le 1$, i.e. the Brauer group Br$(E…

Let $p$ be a prime number and $(K, v)$ a Henselian valued field with a residue field $\widehat K$. This paper determines the Brauer $p$-dimension of $K$, in case $p \neq {\rm char}(\widehat K)$ and $\widehat K$ is a $p$-quasilocal field…

Let $E$ be a field, $p$ a prime number and $F/E$ a finitely-generated extension of transcendency degree $t$. This paper shows that if the absolute Galois group $\mathcal{G}_{E}$ is of nonzero cohomological $p$-dimension cd$_{p}(E)$, then…

Let $E$ be a field of absolute Brauer dimension abrd$(E)$, and $F/E$ a transcendental finitely-generated extension. This paper shows that the Brauer dimension Brd$(F)$ is infinite, if abrd$(E) = \infty $. When the absolute Brauer…

Let $(K, v)$ be a Henselian field with a residue field $\widehat K$ and value group $v(K)$, and let $\mathbb{P}$ be the set of prime numbers. This paper finds conditions on $K$, $v(K)$ and $\widehat K$ under which every algebraic…

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…

We use Kato's Swan conductor to systematically investigate the Brauer $p$-dimension of henselian discretely valued fields of residual characteristic $p>0$. We transform the period-index problem of these fields into the symbol length problem…

Let K be a complete discretely valued field of characteristic 0 with residue field k of characteristic p. Let n=[k:k^p] be the p-rank of k. It was proved by Parimala and Suresh that the Brauer p-dimension of K lies between n/2 and 2n. For…

Let $(K, v)$ be a Henselian valued field satisfying the following conditions, for a given prime number $p$: (i) central division $K$-algebras of (finite) $p$-primary dimensions have Schur indices equal to their exponents; (ii) the value…

We use Kato's Swan conductor to study the Brauer $p$-dimension of fields of characteristic $p>0$. We mainly investigate two types of fields: henselian discretely valued fields and semi-global fields. While investigating the Brauer…

Let $K$ be a global or local field, $E/K$ a Galois extension, and Br$(E)$ the Brauer group of $E$. This paper shows that if $K$ is a local field, $v$ is its natural discrete valuation, $v'$ is the valuation of $E$ extending $v$, and $q$ is…

Given a $(0,p)$-mixed characteristic complete discrete valued field $\mathcal{K}$ we define a class of finite field extensions called \emph{pseudo-perfect} extensions such that the natural restriction map on the mod-$p$ Milnor $K$-groups is…

Let p be a fixed prime number. Let K be a totally real number field of discriminant D\_K and let T\_K be the torsion group of the Galois group of the maximal abelian p-ramified pro-p-extension of K (under Leopoldt's conjecture). We…

We give a formula for the essential dimension of a cohomology class $\alpha$ in $H^d(K, \mathbb{Q}_p/\mathbb{Z}_p (d))$ when $K$ is a strictly Henselian field. This formula is particularly explicit in the case, where $\alpha$ is a Brauer…

Let $E$ be an algebraic extension of a global field $E_{0}$ with a nontrivial Brauer group Br$(E)$, and let $P(E)$ be the set of those prime numbers $p$, for which $E$ does not equal its maximal $p$-extension $E(p)$. This paper shows that…

Let $E$ be a field satisfying the following conditions: (i) the $p$-component of the Brauer group Br$(E)$ is nontrivial whenever $p$ is a prime number for which $E$ is properly included in its maximal $p$-extension; (ii) the relative Brauer…

We study the Brauer group of an abelian variety A over an algebraically closed field of characteristic p focusing on the p-primary torsion, the key part of which is a certain quasi-algebraic unipotent group U_A. We determine its dimension…