GIT quotient

In algebraic geometry, an affine GIT quotient, or affine geometric invariant theory quotient, of an affine scheme ${\displaystyle \operatorname {Spec} A}$ with action by a group scheme G is the affine scheme ${\displaystyle \operatorname {Spec} (A^{G})}$, the prime spectrum of the ring of invariants of A, and is denoted by ${\displaystyle X/\!/G}$. A GIT quotient is a categorical quotient: any invariant morphism uniquely factors through it.

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