In the context of algebraic geometry, particularly when discussing elliptic curves over finite fields, the characteristic refers to a fundamental property of a field that dictates how addition and multiplication interact within that field. Specifically, it is defined as the smallest positive integer 'p' such that adding the number 1 to itself 'p' times results in zero; if no such integer exists, the characteristic is zero. This concept plays a crucial role in understanding the structure of elliptic curves and their points over finite fields.
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