The main object in this chapter (from Section 7.2 onwards) is a quadratic space (M,q) that is decomposed into a direct sum of a totally isotropic submodule U such that U = U⊥, and any supplementary submodule V. Thus (M,q) is hyperbolic (see (2.5.5)) even if V is not totally isotropic, and d q induces canonical isomorphisms U → (M/U⊥)* → V* and V → M/U⊥ → U* (see (2.3.7)). As a quadratic module, V will also interest us, and the short notation (V, q) (instead of (V, q|v)) will be preferred; it is clear that the quadratic form q on M is determined by its restriction to V and by the above isomorphism U → V*.
KeywordsBilinear Form Local Ring Direct Summand Hyperbolic Space Left Ideal
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