I apologize in advance is this is not the correct “category” for this discussion. Please feel free to fix this.

Under the *realization functors* subsection of the entry on motivic homotopy theory, the last line reads:

“For a non-separably closed field k, there is a Gal(k^sep/k)-equivariant realization analogous to the Real realization.”

However no reference is given, and I do not believe such a reference exists. This is an extremely subtle point. See for example Wickelgren’s paper:

http://people.math.gatech.edu/~kwickelgren3/papers/Etale_realization.pdf

This does work in the unstable setting, but this is currently being written up by myself and Elden Elemanto, and we are working on the stable result. I’m not sure the best way to revise this entry. But for sure, if there is a reference, it should be added, and otherwise, I would suggest removing or rephrasing this sentence.

]]>I have created a table

and included it into the relevant entries.

It looks like this:

geometric context | universal additive bivariant (preserves split exact sequences ) | universal localizing bivariant (preserves all exact sequences) | universal additive invariant | universal localizing invariant |
---|---|---|---|---|

noncommutative algebraic geometry | noncommutative motives $Mot_{add}$ | noncommutative motives $Mot_{loc}$ | algebraic K-theory | non-connective algebraic K-theory |

noncommutative topology | KK-theory | E-theory | operator K-theory | … |

I am not sure what should go in the bottom right corner.

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