Work

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

Year: 2025

Type: article

Abstract: We describe the modulo $2$ de Rham-Witt complex of a field of characteristic $2$ , in terms of the powers of the augmentation ideal of the $\mathbb {Z}/2$ -geometric fixed points of real topological restriction homology ${\mathrm {TRR}}$ . This is analogous to the conjecture of Milnor, proved in [Kat82] for fields of characteristic $2$ , which describes the modulo $2$ Milnor K-theory in terms of the powers of the augmentation ideal of the Witt group of symmetric forms. Our proof provides a somewhat explicit description of these objects, as well as a calculation of the homotopy groups of the geometric fixed points of ${\mathrm {TRR}}$ and of real topological cyclic homology, for all fields.

Source: Forum of Mathematics Sigma

DOI: 10.1017/fms.2025.40

Author: Emanuele Dotto

Language: English

Topic: Homotopy and Cohomology in Algebraic Topology

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,650

Funder: Engineering and Physical Sciences Research Council

Award: Characteristic polynomials for symmetric forms