Tag: class-field-theory

54 Intuition for Group Cohomology 2010-01-06T04:19:01.927

54 Please check my 6-line proof of Fermat's Last Theorem. 2010-01-29T22:02:26.687

53 Why are powers of $\exp(\pi\sqrt{163})$ almost integers? 2009-11-09T21:24:18.197

51 Shortest/Most elegant proof for $L(1,\chi)\neq 0$ 2010-05-24T19:39:29.327

50 Learning Class Field Theory: Local or Global First? 2009-11-27T04:51:24.633

48 Erratum for Cassels-Froehlich 2010-01-11T15:20:34.400

37 Topological Langlands? 2009-11-30T15:32:20.337

37 A three-line proof of global class field theory? 2016-09-10T00:38:53.860

36 Why is Class Field Theory the same as Langlands for GL_1? 2011-05-30T23:38:48.870

36 Degree 17 number fields ramified only at 2 2014-06-18T17:49:05.203

32 Motivating Lubin-Tate theory 2015-10-13T14:45:28.663

31 Integers not represented by $ 2 x^2 + x y + 3 y^2 + z^3 - z $ 2010-01-21T02:40:20.793

30 $A_5$-extension of number fields unramified everywhere 2010-11-04T10:33:01.673

28 Artin reciprocity $\implies $ Cubic reciprocity 2016-03-23T17:36:03.860

27 A problem of Shimura and its relation to class field theory 2009-12-31T00:42:01.253

25 Elementary Aspects of Galois Deformation 2010-03-01T19:51:41.343

24 tips on cohomology for number theory 2009-12-11T20:12:59.703

23 Chapters 1--4 of the Artin-Tate notes on Class Field Theory 2010-10-14T07:35:20.910

22 Why do congruence conditions not suffice to determine which primes split in non-abelian extensions? 2010-01-13T19:43:46.517

22 Suggestions for good books on class field theory 2010-05-15T10:17:50.583

22 Any open Langlands Conjectures for GL_1? 2016-09-01T23:42:49.853

21 Most "natural" proof of the existence of Hilbert class fields 2010-10-08T14:01:10.453

21 Are class numbers encoded in the absolute Galois group of ${\mathbb Q}$? 2010-12-20T13:27:49.360

21 A reference for geometric class field theory? 2011-08-17T12:21:02.050

21 Primes of the form $x^2+ny^2$ and congruences. 2011-10-28T02:07:09.433

20 Can one prove complex multiplication without assuming CFT? 2012-06-21T19:25:21.463

20 On the history of the Artin Reciprocity Law 2016-07-03T17:58:48.750

18 Where does the principal ideal theorem (from CFT) go? 2011-04-29T19:57:07.323

18 Class number parity in pure cubic number fields 2011-07-11T15:54:50.703

17 What's the Hilbert class field of an elliptic curve? 2010-02-21T21:21:14.100

17 Kummer generator for the Ribet extension 2010-09-06T12:56:24.400

17 L'un des problèmes fondamentaux de la théorie des nombres 2010-10-06T16:45:23.437

16 Embedding number fields in fields with class number 1 2012-03-26T07:45:20.227

16 Lubin-Tate vs cohomological approach to local CFT 2012-05-08T15:58:39.977

16 What is the "ray" in ray class group? 2012-07-09T02:28:39.697

15 An explicit computation in class field theory 2010-10-20T00:41:02.117

14 Given a number field $K$, when is its Hilbert class field an abelian extension of $\mathbb{Q}$? 2010-02-19T03:48:45.217

14 Elliptic Curves with CM and Class Field Theory 2012-08-30T13:06:59.507

14 Positive binary quadratic form plus univariate monic cubic (giving Hilbert class field) 2014-10-27T01:48:35.597

14 Quickest and/or most elementary proof of "principal iff splits completely"? 2015-05-29T08:08:27.147

13 What is the Hilbert class field of a cyclotomic field? 2009-10-18T01:04:09.657

13 Solvable class field theory 2009-11-06T13:42:04.103

13 Central simple algebras approach to classfield theory, Merits of. 2010-02-05T15:52:37.523

13 Capitulation in cyclotomic extensions 2010-09-28T14:36:30.053

13 Is there an elegant algebraic proof of this formula for quadratic field discriminants? 2011-05-10T05:00:53.003

13 Help wanted with Chebotarev condition in characteristic 2 2011-05-18T02:08:21.253

13 Class groups in dihedral extensions - some sort of Spiegelungssatz? 2011-08-17T05:28:27.440

13 What is the "reason" for modularity results? 2011-09-13T17:18:54.667

13 comparison of completion and Henselization in class field theory 2015-09-05T18:09:38.530

12 Ideal classes fixed by the Galois group 2014-07-30T05:17:49.953

11 Reference for Learning Global Class Field Theory Using the Original Analytic Proofs? 2009-12-09T14:11:24.957

11 On the relation of special values of motivic L functions and partial zetas 2010-11-30T18:20:35.913

11 What numbers are integrally represented by $4 x^2 + 2 x y + 7 y^2 - z^3$ 2012-08-17T03:31:48.677

11 The Class Number One Problem for Real Quadratic Fields 2012-09-06T21:55:32.290

11 How did Takagi prove Kronecker's Jugendtraum for Q(i)? 2013-03-31T18:58:26.380

11 Class field towers 2015-04-23T06:28:26.507

11 Easy cases of Herbrand's theorem 2018-11-15T20:10:34.293

10 Is there an analog of class field theory over an arbitrary infinite field of algebraic numbers? 2010-04-02T14:51:58.130

10 How does one understand geometric CFT in terms of modularity? 2012-06-29T21:38:38.843

10 Cubic fields correspond to $3$-torsion ideals in quadratic fields, or to order $3$ characters of quadratic class groups? 2014-08-28T23:13:51.807

10 What are the current trends in class field theory? 2015-04-30T18:47:21.900

10 What are "Artin fractions"? 2015-12-22T19:16:28.233

10 Parametrizing all cyclic extensions of the rational numbers of degree 5 2016-03-02T16:43:47.527

10 What are the primes that are ramified? 2018-01-26T04:38:53.657

10 A formal group scheme in explicit local class field theory 2018-02-22T02:04:38.917

10 What are the possible bad reductions for an abelian variety of dimension $g$ and a maximal endomorphism ring? 2018-07-02T19:13:57.220

9 Origins of functional field arithmetic 2010-02-25T01:44:59.560

9 Extending methods from Lubin-Tate theory 2010-04-18T23:16:31.283

9 transfer kernels and the Schur multiplier 2011-01-29T18:02:26.817

9 class numbers of $\mathbf{Q}(2^{1/n})$ 2012-02-12T17:29:38.347

9 Hilbert Class Field Galois over Q? 2014-04-11T18:00:03.987

9 Relationship between the conductor of an order and the conductor of a number field extension 2015-09-10T02:09:40.360

8 Where can I find online copies of class field theory publications by Kronecker, Weber, Chevalley, Hasse, Hilbert, Takagi, etc? 2010-02-24T01:34:12.557

8 Is there a notion of Galois extension for Z / p^2? 2010-04-08T19:20:08.510

8 Class Field Theory for Imaginary Quadratic Fields 2010-04-30T10:38:26.287

8 On the structure of the maximal abelian Galois group of a number field 2011-01-21T16:18:58.293

8 Numbers integrally represented by a ternary cubic form 2013-04-11T00:19:00.323

8 Deciding a quadratic diophantine equation 2015-04-05T10:16:04.153

8 Unramified extensions of quadratic fields 2015-12-21T03:22:16.737

8 How to compute with the Stark conjectures? 2017-05-04T14:34:26.197

8 Does Ribet's construction of class fields give us eigenspaces of rank 1? 2017-07-15T23:42:29.617

8 Tables of class numbers of cyclotomic fields 2018-03-05T00:38:12.957

7 remark in milne's class field theory notes 2010-01-28T06:43:41.027

7 Algorithm for the class field tower problem? 2010-04-23T05:33:00.510

7 Explicit map for Scholz reflection principle 2010-10-03T01:55:44.337

7 Maximal (non-abelian) extensions of number fields unramified everywhere 2011-01-27T19:42:34.973

7 Recovering Hecke L-series from Artin L-functions 2011-06-07T22:40:42.773

7 What makes Geometric CFT easier than CFT? 2012-06-27T18:49:47.417

7 n-dimensional local fields 2014-01-10T07:48:33.097

7 Galois groups and prescribed ramification 2014-09-24T07:11:42.020

7 Does the fundamental group identify group structure on subvarieties of products of curves? 2015-03-12T20:57:41.397

7 Minimal Discriminants 2015-06-05T13:57:50.533

7 A prime ideal $\mathfrak{p}$ decomposes in $\mathbb{Q}(\zeta_{24})/\mathbb{Q}(\sqrt{-6})$ iff it is generated by $\alpha\in1+2\Bbb{Z}[\sqrt{-6}]$ 2016-03-26T18:06:49.480

7 Globalizing local field extensions with controlled ramification 2016-05-21T00:03:50.623

7 Existence of imaginary quadratic fields of class numbers coprime to $p$ with prescribed splitting behaviour of $p$ 2016-08-01T11:14:43.933

7 Is cohomology of groups all about $H^{i}: -2\leq i\leq 2$? 2016-08-23T11:13:05.917

7 Explicit $H^2(K, \mu) = Q/Z$? 2017-11-14T15:28:49.823

6 Image of norm map for local field 2011-02-14T08:54:40.813

6 Parity of class number of pure cubic fields 2012-02-04T23:26:32.953