A Generalized Contou-Carrère Symbol and its Reciprocity Laws in Higher Dimensions

Oliver Braunling, Michael Groechenig, Jesse Wolfson

We generalize the theory of Contou-Carrère symbols to higher dimensions. To an $(n+1)$-tuple $f_0,\dots ,f_n\in A((t_1))\cdots ((t_n){)}^{\times }$, where $A$ denotes a commutative alg…