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created a minimum at higher local field and higher arithmetic geometry and added disambiguation with “E-∞ arithmetic geometry”.
The comment at the wikipedia page on higher local fields that
The appropriate replacement for the multiplicative group becomes the nth Milnor K-group
resonates with the slow and on-going discussion here at MO about an algebraic String 2-group (where we should take $n=2$). Henriques says that the appropriate thing is an extension of an algebraic group $G$ by $K_2$, rather than look for 2-group extensions by $\mathbf{B}U(1)$ (which, due to torsionness of the appropriate cohomology groups, won’t correspond to the thing one gets in the smooth setting).
However, the relevant section at wikipedia is a bit vague: which multiplicative group? Of the 2-dimensional local field? Of the base field? I will dig further.
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