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In this paper, Felix, Halperin and Thomas define the notion of a Gorenstein space over a field $\mathbb{k}$: An augmented differential graded algebra $R$ over $\mathbb{k}$ is Gorenstein if $\text{Ext}...

I asked the below question here on MSE, but after some time and a bounty offering I have not received an answer. A graded commutative, connected $\mathbb{k}$-algebra $A$ is called a Poincaré duality ...

1) The category of affine varieties over $\mathbb{C}$ is equivalent to the opposite category of finitely generated reduced algebras over $\mathbb{C}$. The equivalence associates to an affine variety ...