63 What are the local Langlands conjectures nowadays, for connected reductive groups over a $p$-adic field? 2010-02-09T12:28:48.943

32 What are the possible motivic Galois groups over $\mathbb Q$? 2013-04-15T15:15:53.703

30 Introductory text on Galois representations 2011-10-05T19:23:34.443

28 nonabelian reciprocity law 2017-03-02T22:18:38.023

26 Fontaine-Mazur for GL_1 2010-07-25T11:17:29.433

26 Iwasawa main conjectures vs Bloch-Kato conjectures 2010-12-13T15:49:04.107

25 Does the image of a p-adic Galois representation always lie in a finite extension? 2010-03-10T23:03:35.093

25 Modern proof of Serre's open image theorem? 2012-09-26T15:02:32.520

24 Number theory textbook based on the absolute Galois group? 2010-02-12T04:05:31.673

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

22 Where can I find a comprehensive list of equations for small genus modular curves? 2010-02-03T21:12:01.973

22 Subgroups of GL(2,q) 2012-03-19T18:37:45.293

22 Is there a "Langlands philosophy" reason for the fact that the L-function of the Jacobi theta function is (almost) the Riemann zeta function? 2017-03-26T07:48:09.160

21 One dimensional (phi,Gamma)-modules in char p 2010-02-20T16:10:25.777

19 Status of conjectures in Serre's 1969 expose on Galois representations on l-adic cohomology 2012-02-17T00:03:15.957

19 Eichler-Shimura over Totally Real Fields 2013-12-03T12:48:21.903

19 Status of Fontaine-Mazur conjecture 2015-06-09T12:45:19.323

18 Fontaine's rings of periods 2011-04-20T20:08:18.820

17 Applications of Artin's holomorphy conjecture 2010-01-11T17:23:32.957

17 The difficulties in proving modularity lifting theorems over non-totally real fields 2010-01-20T15:17:55.993

17 $p$-adic Langlands correspondence 2011-04-15T01:33:20.560

16 About isogeny theorem for elliptic curves 2010-10-12T18:45:04.353

16 Are there Maass forms where the expected Galois representation is $\ell$-adic? 2012-06-05T22:22:31.050

16 To what extent are modular parametrizations expected to generalize? 2015-09-07T08:36:00.910

16 Is every $GL_2(\mathbb{Z}/n\mathbb{Z})$-extension contained in some elliptic curve's torsion field? 2017-07-12T17:30:27.363

16 Finiteness of Galois cohomology 2018-02-05T18:29:04.390

15 Obstructions to descend Galois invariant cycles 2010-01-13T04:10:54.577

15 Galois representations attached to newforms 2010-02-07T16:40:46.740

15 If the tensor product of two representations are crystalline, are the original representations crystalline? 2010-04-29T17:00:58.457

15 Special values of Artin L-functions 2010-10-07T03:01:59.187

15 Galois representations attached to Maass form 2012-02-29T11:27:54.007

15 Are there known cases of the Mumford–Tate conjecture that do not use Abelian varieties? 2014-11-24T14:17:30.110

15 What are the strongest conjectured uniform versions of Serre's Open Image Theorem? 2015-04-24T04:03:25.780

15 Even Galois representations "mod p" 2015-11-12T04:44:19.200

14 Is there a Montgomery's conjecture for Dirichlet characters and Artin representations ? 2012-12-04T19:43:45.810

14 Why does $H^i(X_{ét},\mathbb{Q}_p)$ have a Hodge-Tate structure? 2013-09-08T15:31:04.960

14 Local-global principle for split extensions of Galois representations 2014-05-01T17:01:02.823

14 Explicit Chebotarev and Langlands - irreducibility of X^5-X-1 mod primes 2015-08-10T13:40:59.793

13 Galois theory and rational points on elliptic curves 2009-12-16T14:26:18.633

13 Period rings for Galois representations 2011-02-07T23:06:48.480

13 Deligne's letter to Jean-Pierre Serre 2011-11-23T19:11:51.123

13 Representations attached to p-adic modular forms 2012-09-28T14:54:12.507

13 What is the classification of characters in $p$-adic Hodge theory? 2013-08-27T19:40:58.633

13 Is there a yoga of effectivity for motives and their realizations? 2014-05-31T10:46:46.993

13 Elliptic curves and supercuspidal representations of conductor $p^2$ 2015-05-08T16:12:04.623

13 When is the image of a 2-dim l-adic representation associated to a modular form open 2015-10-14T03:00:02.490

12 When is the Galois representation on the étale cohomology unramified/Hodge-Tate/de Rham/crystalline/semistable? 2010-03-12T16:30:02.273

12 partition functions and Galois representations? 2011-01-23T09:35:50.697

12 how irregular can a $p$-adic Galois representation be? 2011-03-09T14:05:46.720

12 Why is there a weight 2 modular form congruent to any modular form 2011-07-08T11:47:16.947

12 Is there a "trianguline period ring", or is one expected? 2011-07-13T21:08:25.413

12 Why doesn't functoriality immediately imply the modularity theorem? 2012-10-26T08:24:18.420

12 Best bounds toward Serre's uniformity conjecture 2013-05-02T15:28:15.500

12 Is there literature on approaching semisimplicity of l-adic cohomology using vanishing cycles 2014-05-23T10:04:24.030

12 Applications of anabelian geometry to Galois representations? 2014-08-18T02:24:10.383

12 Which degree does a motivic Galois representation show up in? 2015-06-19T02:49:34.243

12 Propagation of modularity and the Artin conjecture 2015-10-15T06:54:58.393

11 Potential semi-stability of etale cohomology of etale covers. 2010-04-25T20:25:40.777

11 Galois action on one-dimensional quotients of l-adic cohomology 2011-01-29T03:53:27.113

11 Reference for: CM Hilbert Modular forms arise from Hecke characters 2012-05-15T14:50:28.610

11 Serre's Open Image Theorem Without Shafarevich's Theorem 2012-07-18T21:51:30.400

11 Hodge–Tate structures of modular forms 2015-06-23T15:10:43.047

10 Level raising by prime powers 2009-11-05T16:35:46.027

10 Motivation for uniform surjectivity of mod l representations associated to elliptic curves 2009-11-23T05:48:17.587

10 Galois group of a product of polynomials 2010-02-08T20:11:44.117

10 What geometric properties do properties of ell-adic Galois representations imply? 2010-03-12T20:33:16.930

10 What is the etymology for the term conductor? 2010-03-25T02:52:53.267

10 Does the p-adic Tate module of an elliptic curve with ordinary reduction decompose? 2010-06-02T07:53:24.843

10 Are Kato's zeta elements integral? 2010-11-23T19:00:06.657

10 Automorphic forms and Galois representations over imaginary quadratic fields: generalizing Taylor's theorem? 2011-01-02T22:41:26.073

10 Tamely ramified p-adic Galois representations 2011-01-20T15:05:19.970

10 Mod m versions of the toric part of Tate modules 2011-05-16T13:36:54.747

10 Carayol via the trace formula 2011-06-04T15:03:59.300

10 Motives from the fundamental group made nilpotent 2011-07-04T12:32:40.187

10 Cohomology of $SL_2(\mathbb{F}_p)$ acting on trace zero matrices over $\mathbb{F}_p$ 2011-10-12T19:07:03.440

10 "Purely local" proof of local Langlands 2012-05-08T22:28:27.830

10 Effective Chebotarev without Artin's conjecture 2013-05-23T02:11:22.867

10 Galois representations for the curve $y^{2} = x^{3} - x$ 2015-12-09T15:45:39.167

10 $K[[X_1,...]]$ is a UFD (Nishimura's Theorem) 2018-02-19T06:18:19.217

9 Does Ribet's level lowering theorem hold for prime powers? 2009-10-18T01:05:46.037

9 In what sense (if any) does the cohomology of profinite groups commute with projective limits? 2010-04-08T18:53:43.290

9 P-adic local Langlands for non-unitary representations? 2010-04-26T16:07:09.400

9 On the determinant of an odd, continuous Galois representation. 2011-01-19T22:26:38.837

9 Tamagawa numbers of crystalline Galois representations 2011-05-24T11:37:14.283

9 The significance of modularity for all Galois representations 2012-10-04T18:40:44.433

9 What is a(n algebro-geometric) family of modular forms? 2013-02-04T10:00:42.050

9 Langlands program beyond CM fields? 2013-12-25T15:35:55.397

9 Irreducibility of Galois representations attached to unitary groups 2014-05-13T17:58:53.990

9 Eichler-Shimura congruence 2014-11-20T20:06:20.823

9 abelian $\ell$-adic representations in $\widehat{SL(2,Z)}$ 2014-12-17T23:22:50.420

8 number of irreducible representations over general fields 2010-01-01T07:01:30.090

8 Images of action of Galois on the Tate module of Elliptic Curve, 2010-05-07T01:35:24.107

8 When do the Galois reps of modular forms have open image? 2010-05-10T10:20:46.240

8 Can an etale (phi, Gamma) module be an extension of non-etale ones? 2010-10-24T11:11:35.183

8 Explicitly describing a two-dimensional reducible representation of G_{Q_p} 2010-12-15T03:00:44.897

8 Semistable Elliptic Curves and irreducible Galois representations 2011-05-09T08:36:32.987

8 Do Tamagawa numbers of Galois representations stabilise in the cyclotomic tower? 2011-05-19T16:10:00.643

8 Image of complex conjugation by modular representations in characteristic 2 2011-10-20T16:54:11.690

8 P-adic representations 2011-11-10T21:04:54.123