A group scheme is an algebraic object that generalizes the notion of a group in the context of schemes, allowing one to define group operations like multiplication and inversion in a way that respects the structure of schemes. It is characterized by a functor from the category of schemes to the category of groups, providing a way to study algebraic groups using the language of algebraic geometry. This concept plays a significant role in understanding various properties and behaviors of algebraic groups over different fields.
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