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The moduli space of commutative algebras of finite rank

Bjorn Poonen (2008)

Journal of the European Mathematical Society

The moduli space of rank- n commutative algebras equipped with an ordered basis is an affine scheme 𝔅 n of finite type over , with geometrically connected fibers. It is smooth if and only if n 3 . It is reducible if n 8 (and the converse holds, at least if we remove the fibers above 2 and 3 ). The relative dimension of 𝔅 n is 2 27 n 3 + O ( n 8 / 3 ) . The subscheme parameterizing étale algebras is isomorphic to GL n / S n , which is of dimension only n 2 . For n 8 , there exist algebras that are not limits of étale algebras. The dimension calculations...

Zero-Dimensionality and Serre Rings

Karim, D. (2004)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: Primary 13A99; Secondary 13A15, 13B02, 13E05.This paper deals with zero-dimensionality. We investigate the problem of whether a Serre ring R <X> is expressible as a directed union of Artinian subrings.

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