标题： 关于高斯复合的正交观点 显示英文标题

标题： An orthogonal perspective on Gauss composition

摘要： 我们重新审视在一般基概形上的高斯复合，重点在于正交群。 我们证明克莱夫福德和范数函子在二元二次模和二次代数上的伪正规模之间提供了保持判别式的范畴等价。 这种观点综合了Kneser和Wood的构造，调和了代数和几何方法，并阐明了方向的作用以及狭义类群的自然出现。 作为应用，我们限制到格，并证明二元正交特征形式对应于Hecke字符。 显示英文摘要

摘要： We revisit Gauss composition over a general base scheme, with a focus on orthogonal groups. We show that the Clifford and norm functors provide a discriminant-preserving equivalence of categories between binary quadratic modules and pseudoregular modules over quadratic algebras. This perspective synthesizes the constructions of Kneser and Wood, reconciling algebraic and geometric approaches and clarifying the role of orientations and the natural emergence of narrow class groups. As an application, we restrict to lattices and show that binary orthogonal eigenforms correspond to Hecke characters.