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math.CO2026
Coloring Monomial Cayley Graphs: The One-Parameter Case
Jonathan Davidson
How do algebraic relations among unit directions influence the chromatic number of the plane? We introduce monomial Cayley graphs as a framework for investigating this question, be…
math.NT2026
On semi-stable integral models for Shimura varieties
Jie Yang, Ioannis Zachos, Zhihao Zhao
We construct (potentially) semi-stable integral models for a class of Shimura varieties with maximal parahoric level at an odd prime . The main input is an explicit construction…
math.NT2026
On -adic integral moduli schemes and local models for PEL type D
Jie Yang, Ioannis Zachos, Zhihao Zhao
We construct flat integral moduli schemes of PEL type D and the corresponding flat orthogonal Rapoport--Zink spaces with parahoric level structure over a -adic integer ring. The…