An analogue of the Milnor conjecture for the de Rham-Witt complex in characteristic 2

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• Emanuele Dotto (University of Warwick)
• Monday 13 January 2025, 15:30-16:30
• Seminar Room 1, Newton Institute.

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EHTW01 - Introductory Workshop for Equivariant Homotopy Theory in Context

The Milnor conjecture relates the mod 2 Milnor K-theory of a field and the fundamental ideal of the Witt group of symmetric forms over that field. The conjecture was proved by Kato for fields of characteristic 2, and by Orlov-Vishik-Voevodsky in all other characteristics, and was at the heart of Voevodsky’s development of motivic homotopy theory. The first part of the talk will give a basic overview of the objects involved in this result, and of their relationship to trace maps in algebraic K-theory. We will then, via a questionable interpretation of the Minor conjecture via equivariant homotopy theory, formulate an analogue of the conjecture for Illusie’s de Rham-Witt complex. This conjecture can then be proved from some explicit calculations of the real topological cyclic homology of fields.

This talk is part of the Isaac Newton Institute Seminar Series series.

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