4 papers
On Bounds of Extension Degrees for Similarity of Integral Matrices over Number Fields
Mingqiang Feng, Ziyang Zhu
It is well-known that if integral matrices and of a number field are similar over all completions of the ring of integers of , then and are simil…
Conjugacy of Isometries in Real Orthogonal Groups
Ziyang Zhu
We determine all orthogonal transformations of a quadratic space over reals such that any orthogonal transformation which is conjugate to one of them in the linear group is conjuga…
Riemann-Hurwitz Formula for Arithmetic Surfaces
Ziyang Zhu
In this paper, we presents a method for factoring morphisms between arithmetic surfaces based on the regularity of arithmetic surfaces. Using this factorization, we derive a Rieman…
Similarity of Matrices over Dedekind Rings
Ziyang Zhu
We extend Latimer and MacDuffee's theorem to a general commutative domain and apply this result to study similarity of matrices over integral rings of number fields. We also conjec…