Variants of normality and steadfastness deform

Autor:	Bauman, Alexander, Ellers, Havi, Hu, Gary, Murayama, Takumi, Nair, Sandra, Wang, Ying
Rok vydání:	2022
Předmět:	Mathematics - Commutative Algebra Mathematics - Algebraic Geometry 13F45 13B25 (Primary) 14B07 13B22 13F25 (Secondary)
Druh dokumentu:	Working Paper
Popis:	The cancellation problem asks whether $A[X_1,X_2,\ldots,X_n] \cong B[Y_1,Y_2,\ldots,Y_n]$ implies $A \cong B$. Hamann introduced the class of steadfast rings as the rings for which a version of the cancellation problem considered by Abhyankar, Eakin, and Heinzer holds. By work of Asanuma, Hamann, and Swan, steadfastness can be characterized in terms of $p$-seminormality, which is a variant of normality introduced by Swan. We prove that $p$-seminormality and steadfastness deform for reduced Noetherian local rings. We also prove that $p$-seminormality and steadfastness are stable under adjoining formal power series variables for reduced (not necessarily Noetherian) rings. Our methods also give new proofs of the facts that normality and weak normality deform, which are of independent interest. Comment: 22 pages. Comments welcome! v2: Minor changes
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2202.00163 Zobrazit plný text záznamu View this record from Arxiv