Year: 2026
Type: article
Abstract: There exist results proving that within certain families of totally real number fields, the minimal rank of a universal quadratic lattice over such a field can be arbitrarily large. Kala introduced a technique of extending such results to larger fields — e.g., from quadratic fields to fields of arbitrary even degree — under some conditions. We present improvements to this technique by investigating the structure of subfields within the smallest common superfield of two number fields, using Galois theory to translate this into a group-theoretic problem. In particular, we show that if totally real number fields with minimal rank of a universal lattice [Formula: see text] exist in degree d, then they also exist in degree [Formula: see text] for all [Formula: see text].
Author: Matěj Doležálek
Institution: Charles University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Univerzita Karlova v Praze
OpenAlex ID: W7124417189