What does this research mean for the field?

The K-groups of the affine boundary quotient attached to a principal prime of a number field incorporate the norm and trace of the uniformizer, and unexpectedly depend on the unit orbit of the uniformizer rather than being canonical in the prime. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

Calculate the K-theory groups of the affine boundary quotient associated with a principal prime in an algebraic number field.

September 8, 2026Open Access

K-theory of the affine boundary quotient: the return of the norm and the trace

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Authors

RCRuqing ChenZhejiang Normal University

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Implication

Theoretical analysis reveals exact torsion invariants in the K-theory of affine boundary quotients for number fields, indicating sensitivity to uniformizer unit orbits and the trace.

Key Points

Calculate the K-theory groups of the affine boundary quotient associated with a principal prime in an algebraic number field.
Represented the affine boundary quotient as a crossed-product C*-algebra over a local field.
Performed an iterated Pimsner-Voiculescu sequence computation along an exterior-power tower using integral adjugate transfers.
The unit class generates a torsion summand of exact order q - 1, attaining the theoretical divisibility bound.
Intermediate exterior layers contribute torsion governed by det(q - Lambda^r pi), yielding Z/|q +- 1 - Tr(pi)| in real quadratic fields where the trace enters the K-theory.
The invariant depends on the unit orbit of the uniformizer rather than the prime alone, identifying ideal class groups as obstructions for non-principal primes.

Cite This Study

Ruqing Chen (2026) studied this question.

synapsesocial.com/papers/6a9fd77658e84d0ff5b46267 https://doi.org/10.5281/zenodo.22427553

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Implication

Theoretical analysis reveals exact torsion invariants in the K-theory of affine boundary quotients for number fields, indicating sensitivity to uniformizer unit orbits and the trace.

K-theory of the affine boundary quotient: the return of the norm and the trace

Discussion

Member takes

Implication

Key Points

Cite This Study

K-theory of the affine boundary quotient: the return of the norm and the trace

Discussion

Member takes

Implication

Key Points

Cite This Study

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