Counterexamples regarding Symmetric Tensors and Divided Powers

Details Counterexamples regarding Symmetric Tensors and Divided Powers Counterexamples regarding Symmetric Tensors and Divided Powers

2007-02-24

arxiv.org/abs/math/0702733v2

Mathematics

Commutative Algebra

22 pages. Updates: Added new section 7, added remarks regarding extension to general characteristic p>0. To appear in Journal

Scientific paper

We investigate the similarities and differences between the module of symmetric tensors TS^n_A(M) and the module of divided powers \Gamma^n_A(M). There is a canonical map \Gamma^n_A(M) \to TS^n_A(M) which is an isomorphism in many important cases. We give examples showing that this map need neither be surjective nor injective in general. These examples also show that the functor TS_A^n does not in general commute with base change.

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