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arXiv · 1109.4088

On the Topologies on ind-Varieties and related Irreducibility Questions

Immanuel Stampfli
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Abstract

In the literature there are two ways of endowing an affine ind-variety with a topology. One possibility is due to Shafarevich and the other to Kambayashi. In this paper we specify a large class of affine ind-varieties where these two topologies differ. We give an example of an affine ind-variety that is reducible with respect to Shafarevich's topology, but irreducible with respect to Kambayashi's topology. Moreover, we give a counter-example of a supposed irreducibility criterion of Shafarevich which is different from a counter-example given by Homma. We finish the paper with an irreducibility criterion similar to the one given by Shafarevich.

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BibTeXRIS

Immanuel Stampfli. 2016-11-23. On the Topologies on ind-Varieties and related Irreducibility Questions. https://doi.org/10.1016/j.jalgebra.2012.08.019

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