What question did this study set out to answer?

The aim is to extend results on the minimal rank of universal quadratic lattices from certain number fields to larger fields.

Extending bounds on minimal ranks of universal quadratic lattices to larger number fields

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This research extends minimal rank findings of quadratic lattices in number fields, suggesting broader implications for higher degrees.

The aim is to extend results on the minimal rank of universal quadratic lattices from certain number fields to larger fields.
Investigated subfield structures within common superfields of two number fields.
Utilized Galois theory to translate findings into a group-theoretic context.
Analyzed conditions under which ranks can be extended to higher degrees.
Demonstrated that the minimal rank of universal lattices can be arbitrarily large in certain higher degree fields.
Established that if lattices exist in degree d, they also exist in degree kd for k ≥ 3, expanding previous results.

Matěj Doležálek (2026) studied this question.

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View Full Paper

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Authors

This research extends minimal rank findings of quadratic lattices in number fields, suggesting broader implications for higher degrees.

The aim is to extend results on the minimal rank of universal quadratic lattices from certain number fields to larger fields.
Investigated subfield structures within common superfields of two number fields.
Utilized Galois theory to translate findings into a group-theoretic context.
Analyzed conditions under which ranks can be extended to higher degrees.
Demonstrated that the minimal rank of universal lattices can be arbitrarily large in certain higher degree fields.
Established that if lattices exist in degree d, they also exist in degree kd for k ≥ 3, expanding previous results.

Matěj Doležálek (2026) studied this question.

View Full Paper

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