arXiv subjects

Marco Sobiech

Publications and source records attributed to Marco Sobiech.

4 recordsLinked to original sources

arXiv2022

Function field extensions and annihilators of differential forms in characteristic p and bilinear forms in characteristic 2

Let $F$ be a field of characteristic $p>0$ and let $Ω^n(F)$ be the $F$-vector space of $n$-differential forms over $F$. In this work we will study the behaviour of $Ω^n(F)$ under iterated function field extensions of $p$-forms. We will use results from a previous work to rewrite the kernel of the restriction map $Ω^n(F) \to Ω^n(F(φ_1,\ldots,φ_r))$ to a set of differential forms annihilated by specific forms given by the norm fields of $φ_1,\ldots,φ_r$. We will close this work by translating the new resluts to the theory of bilinear forms over fields of characteristic $2$.

math.AC↗

arXiv2022

Annihilators of differential forms over over fields of characteristic p

Let $F$ be a field of characteristic $p$ and let $Ω^n(F)$ be the $F$-vector space of $n$-differential forms. In this work, we will study the annihilator of differential forms, give specific descriptions for special cases and show a connection between these annihilators and the kernels of the restriction map $Ω^n(F) \to Ω^n(E)$ for purely inseparable field extensions $E/F$.

math.AC↗

arXiv2016

The behavior of differential, quadratic and bilinear forms under purely inseparable field extensions

Let $F$ be a field of characteristic $p$ and let $E/F$ be a purely inseparable field extension. We study the group $H_p^{n+1}(F)$ of classes of differential forms under the restriction map $H_p^{n+1}(F)\to H_p^{n+1}(E)$ and give a system of generators of the kernel $H_p^{n+1}(E/F)$. In the case $p=2$, we use this to determine the kernel $W_q(E/F)$ of the restriction map $W_q(F) \to W_q(E)$ between the group of nonsingular quadratic forms over $F$ and over $E$. We also deduce the corresponding result for the bilinear Witt kernel $W(E'/F)$ of the restriction map $W(F) \to W(E')$, where $E'/F$ denotes a modular purely inseparable field extension.

math.AC↗

arXiv2014

Witt kernels and Brauer kernels for quartic extensions in characteristic two

Let $F$ be a field of characteristic $2$ and let $E/F$ be a field extension of degree $4$. We determine the kernel $W_q(E/F)$ of the restriction map $W_qF\to W_qE$ between the Witt groups of nondegenerate quadratic forms over $F$ and over $E$, completing earlier partial results by Ahmad, Baeza, Mammone and Moresi. We also deduct the corresponding result for the Witt kernel $W(E/F)$ of the restriction map $WF\to WE$ between the Witt rings of nondegenerate symmetric bilinear forms over $F$ and over $E$ from earlier results by the first author. As application, we describe the $2$-torsion part of the Brauer kernel for such extensions.

math.AC↗