关于对称张量和分幂的反例
Counterexamples regarding Symmetric Tensors and Divided Powers
摘要：
研究了对称张量模TS^n_A（M）与分幂模Γ^n_A（M）之间的异同.存在一个标准映射Γ^n_A（M）\to TS^n_A（M），它在许多重要情况下是同构的.我们给出的例子表明，这个地图既不需要满射，也不内射一般。这些例子也表明函子TS_A^n一般不与基变换交换。
英文摘要：
We investigate the similarities and differences between the module of symmetric tensors TS^n_A(M) and the module of divided powers Γ^n_A(M). There is a canonical map Γ^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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
