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Algebraic varieties with group operations given by morphisms, or group objects in the category of algebraic varieties, the category of algebraic schemes, or closely related categories.

9 votes

Is an algebraic space group always a scheme?

Over a field, the reference is indeed "Algebraization of formal moduli, I". Over a base more general than a field, the answer may be no. For example, Artin proved in "Algebraization of formal moduli, …
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4 votes
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Automorphism group of bi-elliptic surface

The answer is always "no". By classification, a bielliptic surface over $\mathbb C$ has the form $(E\times F)/G$ where $E,F$ are elliptic curves, $G=\subset Aut(E,0)$ is an abelian group acting by com …
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