Revistes Catalanes amb Accés Obert (RACO)

A note on 2-dimensional arithmetic symbols on $\operatorname{Gl}(n,\Sigma_S)$

F. Pablos Romo

Resum


The aim of this note is to offer a summary of the definitions and properties of arithmetic symbols on the linear group $\operatorname{Gl}(n,\mathcal{F})$ ---$\mathcal{F}$ being an arbitrary discrete valuation field---, and to show that the natural generalizations of the Parshin symbol on an algebraic surface $S$ to
the linear group $\operatorname{Gl}(n,\Sigma_S)$ do not allow us to define new $2$-dimensional symbols on $S$.

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