What question did this study set out to answer?

The aim is to determine the finiteness of the normalized trace-class set in a cyclotomic field under specific conditions.

July 23, 2026Open Access

Cyclotomic Trace–Norm Rigidity: An Abstract Framework and a Finiteness Theorem

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This theoretical framework explores finite normalized trace classes in cyclotomic fields, suggesting a significant restriction on trace behavior.

The aim is to determine the finiteness of the normalized trace-class set in a cyclotomic field under specific conditions.
Analyzed relative traces through rational p-adic reduction and primitivization in a quadratic subfield.
Established conditions for finiteness involving trace non-degeneracy and uniform trace support.
Transformed the problem into a non-degenerate S-unit equation for further analysis.
Proved that the normalized trace-class set is finite when certain hypotheses are satisfied, particularly if the degree of K over L is at least 2.
Demonstrated that a norm-square condition acts as a Diophantine filter on the trace class set.

Rogelio Méndez Ibarra (2026) studied this question.

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This theoretical framework explores finite normalized trace classes in cyclotomic fields, suggesting a significant restriction on trace behavior.