The Weil conjectures are a set of important conjectures in algebraic geometry, formulated by André Weil in the mid-20th century. They primarily concern the relationship between algebraic varieties over finite fields and their number of rational points, as well as properties related to their zeta functions. The conjectures are as follows: 1. **Rationality of the Zeta Function**: The zeta function of a smooth projective variety over a finite field can be expressed as a rational function.
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