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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeJun 11th 2014

Over on MO (in the comments here) Stefan Wendt kindly reminds me of an old $n$Lab entry I once started on B1-homotopy theory. Have added a reference and hope to be adding more.

• CommentRowNumber2.
• CommentAuthorDavid_Corfield
• CommentTimeJun 12th 2014

Following the reference to Ayoub there, I see his 2014 ICM talk is available. It begins

The (co)homological invariants associated to an algebraic variety fall into two classes:

(a) the algebro-geometric invariants such as higher Chow groups (measuring the complexity of algebraic cycles inside the variety) and Quillen K-theory groups (measuring the complexity of vector bundles over the variety);

(b) the class of transcendental invariants such as Betti cohomology (with its mixed Hodge structure) and l-adic cohomology (with its Galois representation).

The distinction between these two classes is extreme.

Is this a form of fracturing?

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