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An Unstable Representability Criterion

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If you have a question about this talk, please contact Andreas Holmstrom.

Some (co)homology theories in algebraic geometry arise as homotopy groups of certain auxiliary constructions, for example algebraic K-theory. In these cases, one can give simple sufficient conditions for these theories to be representable in the unstable A1-homotopy category.

The result can be found as Theorem 3.1 in Hornbostel’s paper on A1-representability of Hermitian K-theory. However, the proof I hope to give follows a simpler argument that I learned from Markus Severitt. The main difference to Hornbostel’s treatment is the use of Dugger’s model category rather than Morel/Voevodsky’s.

At the end of my talk, Peter Arndt will give a brief clarification of the notion of an enriched category.

This talk is part of the Motivic stable homotopy theory study group series.

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