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Algebras with the same (algebraic) geometry. (English) Zbl 1062.08012
Proc. Steklov Inst. Math. 242, 165-196 (2003) and Tr. Mat. Inst. Im. V. A. Steklova 242, 176-207 (2003).
Summary: Some basic notions of classical algebraic geometry can be defined on arbitrary varieties of algebras $$\Theta$$. For every algebra $$H$$ in $$\Theta$$, one can consider algebraic geometry in $$\Theta$$ over $$H$$. Correspondingly, algebras in $$\Theta$$ are considered with the emphasis on equations and geometry. We give examples of geometric properties of algebras in $$\Theta$$ and of geometric relations between them. The main problem considered in the paper is when different $$H_1$$ and $$H_2$$ have the same geometry.
For the entire collection see [Zbl 1059.03004].

##### MSC:
 08B99 Varieties 14A20 Generalizations (algebraic spaces, stacks)
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