Synopsis
Chapter 1. Diophantus of Alexandria.- Chapter 2. Algebraic closure; affine space.- Chapter 3. Rational points; finite fields.- Chapter 4. Projective varieties; conics and quadrics.- Chapter 5. The Nullstellensatz.- Chapter 6. Euclidean rings.- Chapter 7. Cubic surfaces.- Chapter 8. p-adic completions.- Chapter 9. The Hasse principle.- Chapter 10. Diophantine dimension of fields.
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