# The image of the spec functor under a restriction

What is the image of the restriction of the Spec functor (the functor from commutative rings to affine schemes) to commutative rings with the trivial monoid under multiplication?

Thanks very much

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Welcome to math.SE: since you are new, I wanted to let you know a few things about the site. In order to get the best possible answers, it is helpful if you say in what context you encountered the problem, and what your thoughts on it are; this will prevent people from telling you things you already know, and help them give their answers at the right level. If this is homework, please add the homework tag; people will still help, so don't worry. –  Julian Kuelshammer Oct 18 '12 at 7:43
Hi Julian, thanks for the comment. I want to find a subcategory of the category of affine schemes that is dual to the category of commutative rings with trivial monoid under multiplication which is equivalent to the category of abelian groups. –  u4953u Oct 18 '12 at 7:48
The dual of the category of abelian groups can be embedded in the category of locally compact abelian groups, by Pontryagin duality. –  Zhen Lin Oct 18 '12 at 8:16