arXiv subjects

A. Soman

Publications and source records attributed to A. Soman.

2 recordsLinked to original sources

arXiv2019

On triviality of reduced Whitehead group over Henselian fields

Let $F$ be a Henselian field of $q$-cohomological dimension $3$, where $q$ is a prime. Let $Γ_F$ be the totally ordered abelian value group of $F$ and let $D$ be a central division algebra over $F$ of index a power of $q$ such that the characteristic of the residue field, $\overline{F}$ is coprime to $q$. We show that when $1\leq\dim_{\mathbb{F}_q}(Γ_F/qΓ_F)\leq 3$, the reduced Whitehead group of $D$ is trivial.

math.RA↗

arXiv2016

Adjoint groups over ${\mathbb Q}_p (X)$ and R-equivalence - revisited

We obtain a class of examples of non-rational adjoint classical groups of type $^2A_n$ and a group of type $^2D_3$ over the function field $F$ of a smooth geometrically integral curve over a $p$-adic field with $p \neq 2$. We also show that for any group of type $C_n$ over $F$, the group of rational equivalence classes of $G$ over $F$ is trivial, i.e., $G(F)/R=(1)$.

math.NT↗