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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeAug 14th 2014
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   Author: Urs
   Format: MarkdownItexcreated a minimum at _[[higher local field]]_ and _[[higher arithmetic geometry]]_ and added disambiguation with "[[E-∞ arithmetic geometry]]".

   created a minimum at higher local field and higher arithmetic geometry and added disambiguation with “E-∞ arithmetic geometry”.

2. • CommentRowNumber2.
   • CommentAuthorDavidRoberts
   • CommentTimeAug 15th 2014
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   Author: DavidRoberts
   Format: MarkdownItexThe comment at the [wikipedia page on higher local fields](http://en.wikipedia.org/wiki/Higher_local_field) 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](http://mathoverflow.net/q/143654/4177) 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.

   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.