Counterexamples regarding symmetric tensors and divided powers

• Autores: Christian Lundkvist
• Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 212, Nº 10, 2008, págs. 2236-2249
• Idioma: inglés
• DOI: 10.1016/j.jpaa.2008.03.024
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• Resumen

  • We investigate the similarities and differences between the module of symmetric tensors and the module of divided powers . There is a canonical map 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 does not in general commute with base change.