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Periodicity of hermitian K-theory and Milnor's K-groups

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Max Karoubi

K-Theory and Homology · Submitted 20 Sep 2005

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Using the solution of Milnor's conjecture by Voevodsky, we show that the non triviality of Milnor's K-groups mod. 2 implies also the non triviality of higher Witt groups (when A is a field).

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arXiv IDmath/0509453 (version 1)
Pith IDMB3GKK4X, Pith's permanent record of this paper and its review
CitationMax Karoubi. "Periodicity of hermitian K-theory and Milnor's K-groups." arXiv:math/0509453 (2005). https://pith.science/paper/MB3GKK4X
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,664 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.46 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.73 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We use recent results proved by Berrick and the author (math.KT/0509404) to improve the periodicity theorem in hermitian K-theory. We define also a new filtration of the classical Witt ring W(A), built from non degenerate quadratic forms over any commutative ring A where 2 is invertible. This filtration is linked to the Milnor and Quillen K-groups. Using the solution of Milnor's conjecture by Voevodsky, we show that the non triviality of Milnor's K-groups mod. 2 implies also the non triviality of higher Witt groups (when A is a field).

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We use recent results proved by Berrick and the author (math.KT/0509404) to improve the periodicity theorem in hermitian K-theory. contribution 0.85 0.75 0.22 asserted 1.00
s1 We define also a new filtration of the classical Witt ring W(A), built from non degenerate quadratic forms over any commutative ring A where 2 is invertible. contribution 1.00 0.95 0.09 asserted 1.00
s2 This filtration is linked to the Milnor and Quillen K-groups. contribution 0.43 0.62 0.08 asserted 1.00
s3 Using the solution of Milnor's conjecture by Voevodsky, we show that the non triviality of Milnor's K-groups mod. 2 implies also the non triviality of higher Witt groups (when A is a field). result 0.95 0.87 0.49 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.89.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We use recent results proved by Berrick and the author (math.KT/0509404) to improve the periodicity theorem in hermitian K-theory. We define also a new filtration of the classical Witt ring W(A), built from non degenerate quadratic forms over any commutative ring A where 2 is invertible. This filtration is linked to the Milnor and Quillen K-groups. Using the solution of Milnor's conjecture by Voevodsky, we show that the non triviality of Milnor's K-groups mod. 2 implies also the non triviality of higher Witt groups (when A is a field).

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