Counterexamples regarding Symmetric Tensors and Divided Powers
交换代数
2008-03-24 v2 代数几何
摘要
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.
引用
@article{arxiv.math/0702733,
title = {Counterexamples regarding Symmetric Tensors and Divided Powers},
author = {Christian Lundkvist},
journal= {arXiv preprint arXiv:math/0702733},
year = {2008}
}
备注
22 pages. Updates: Added new section 7, added remarks regarding extension to general characteristic p>0. To appear in Journal of Pure and Applied Algebra