1 | Absolute values and discrete valuations (PDF) |
2 | Localization and Dedekind domains (PDF) |
3 |
Properties of Dedekind domains, ideal class groups, factorization of ideals (PDF)
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4 |
Étale algebras, norm and trace (PDF)
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5
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Dedekind extensions (PDF)
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6 | Ideal norms and the Dedekind-Kummer thoerem (PDF) |
7 | Galois extensions, Frobenius elements, and the Artin map (PDF) |
8 | Complete fields and valuation rings (PDF) |
9 | Local fields and Hensel's lemmas (PDF) |
10 |
Extensions of complete DVRs (PDF)
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11 | Totally ramified extensions and Krasner's lemma (PDF) |
12 |
The different and the discriminant (PDF)
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13 |
Global fields and the product formula (PDF)
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14 | The Minkowski bound and finiteness results (PDF) |
15 |
Dirichlet's unit theorem (PDF)
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16 |
Riemann's zeta function and the prime number theorem (PDF)
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17 | The functional equation (PDF) |
18 |
Dirichlet L-functions and primes in arithmetic progressions (PDF)
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19 |
The analytic class number formula (PDF)
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20 |
The Kronecker-Weber theorem (PDF)
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21 |
Class field theory: ray class groups and ray class fields (PDF)
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22 |
The main theorems of global class field theory (PDF)
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23 | Tate cohomology (PDF) |
24 |
Artin reciprocity in the unramified case (PDF)
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25 |
The ring of adeles, strong approximation (PDF)
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26 | The idele group, profinite groups, infinite Galois theory (PDF) |
27 |
Local class field theory (PDF)
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28 | Global class field theory and the Chebotarev density theorem (PDF) |