Geodesic
On $n$-ADC integral quadratic lattices over algebraic number fields
Documenta mathematica, Tome 30 (2025) no. 4, pp. 981-1022

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In the paper, we extend the ADC property to the representation of quadratic lattices by quadratic lattices, which we define as n-ADC-ness. We explore the relationship between n-ADC-ness, n-regularity, and n-universality for integral quadratic lattices. Also, for n≥2, we give necessary and sufficient conditions for an integral quadratic lattice over arbitrary non-archimedean local fields to be n-ADC. Moreover, we show that over any algebraic number field F, an integral OF​-lattice with rank n+1 is n-ADC if and only if it is OF​-maximal of class number one.
DOI : 10.4171/dm/1003
Classification : 11E08, 11E12, 11E95
Mots-clés : ADC quadratic forms, universal quadratic forms, regular quadratic forms 
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     author = {Zilong He},
     title = {On $n${-ADC} integral quadratic lattices over algebraic number fields},
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Zilong He. On $n$-ADC integral quadratic lattices over algebraic number fields. Documenta mathematica, Tome 30 (2025) no. 4, pp. 981-1022. doi: 10.4171/dm/1003

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