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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.
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Is SL(2,C)/SL(2,Z) a quasi-projective variety?
No, the quotient is not quasi-projective. In the paper Invariant meromorphic functions on complex semisimple Lie groups by D. N. Ahiezer you can find the following result.
Theorem. Let $G$ be a co …