The symplectic Gram-Schmidt theorem and fundamental geometries for -modules
Like the classical Gram-Schmidt theorem for symplectic vector spaces, the sheaf-theoretic version (in which the coefficient algebra sheaf is appropriately chosen) shows that symplectic -morphisms on free -modules of finite rank, defined on a topological space , induce canonical bases (Theorem 1.1), called symplectic bases. Moreover (Theorem 2.1), if is an -module (with respect to a -algebra sheaf without zero divisors) equipped with an orthosymmetric -morphism, we show, like in the classical...