| 31. | Andr?Weil was especially interested in algebraic geometry over finite fields and other rings.
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| 32. | Let be a curve of genus defined over, the finite field with elements.
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| 33. | While no finite field is infinite, there are infinitely many different finite fields.
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| 34. | While no finite field is infinite, there are infinitely many different finite fields.
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| 35. | For example, all finite fields are perfect.
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| 36. | This is the main motivation to define the cosine transform over prime finite fields.
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| 37. | This group is isomorphic to the absolute Galois group of an arbitrary finite field.
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| 38. | How does this work over a finite field?
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| 39. | The construction also works over finite fields, providing examples in finite projective planes.
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| 40. | The ring of integers modulo is a finite field if and only if is prime.
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