Field Arithmetic |
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Infinite Galois Theory and Profinite Groups | 1 |
Algebraic Function Fields of One Variable | 12 |
2 | 21 |
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a₁ abelian absolutely irreducible absolutely irreducible polynomial algebraic extension algebraically closed Apply Lemma assume B₁ closed fields closed subgroup coefficients compute conclude Consider contains Corollary countable defined degree Denote domain element elementary embedding property epimorphism equivalent exists finite fields finite Galois extension finite groups finite separable extension follows formula Frattini cover function field G₁ Galois extension Galois group group G h₁ Haar measure Hence Hilbert set Hilbertian field homomorphism implies induction infinite integral closure irreducible polynomial isomorphism K-variety L₁ Let F linearly disjoint modulo nonempty nontrivial nonzero normal subgroup open normal subgroup open subgroup perfect PAC field positive integer prime divisor prime ideal primitive recursive profinite group projective Proof Proposition prove regular extension resp ring satisfies Section sentence 9 separable extension sequence subgroup of G subset Suppose t₁ theory ultraproduct valuation variables X₁ Y₁ zero