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[1] [2] [3] [4] [5] [6] [7] [8] Table of Contents.  [9]
1.1 Rigid analytic spaces attached to complete local noetherian rings. 
[10] 1.2. Irreducible components and component parts.  [11]
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l.1086 closure of the morphism i:S \to
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[12] [13] [14] [15] 1.3. Fredholm varieties.  [16] [17] [18] [19] [20] [21]
[22] [23] [24] [25] [26] 1.4 Weight space.  [27] [28]
1.5. The eigencurve as the Fredholm closure of the classical modular locus.\hsk
ip 1em\relax (Statement of the main theorems)  [29] [30] [31] [32] [33]
[34] [35] 2.1 Affinoid sub-domains in modular curves.  [36] [37] [38] [39]
2.2 Eisenstein series.  [40] [41] [42] [43] [44]
2.3. Katz $p$-adic\ Modular Functions.  [45]
2.4 Convergent modular forms and Katz modular functions.  [46] [47]
3.1 Hecke eigenvectors and generalized eigenvectors.  [48] [49]
3.2. Action on $\fam \bffam \tenbf M_k(Np^m,v;K)$.  [50]
3.3 Action on Katz Modular Functions.  [51]
3.4. Action on $\fam \bffam \tenbf M^\dagger (N)$.  [52]
3.5. Action on weight $\kappa $ forms.  [53]
3.6. Remarks about cusp forms and Eisenstein series.  [54]
4.1. Completely continuous operators and Fredholm determinants.  [55] [56]
[57] 4.2. Factoring Characteristic Series.  [58] [59] [60]
4.3. Analytic variation of the Fredholm determinant.  [61] [62] [63] [64]
[65] [66] 4.4 The Spectral Curves.  [67]
5.1. Deforming representations and pseudo-representations.  [68] [69] [70]
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[71] [72] [73] [74] [75] [76] [77] [78] [79] [80]
5.2. Pseudo-representations attached to Katz modular functions.  [81] [82]
[83] 6.1. The definition of the eigencurve.  [84]
6.2. The points of the eigencurve are overconvergent eigenforms.  [85] [86]
[87] [88] 6.3. The projections of the eigencurve to the spectral curves. 
[89] [90] 6.4. The Eisenstein curve.  [91] 7.1. Local pieces.  [92] [93]
[94] 7.2. Gluing.  [95] 7.3. The relationships among the curves $D_\alpha $. 
[96] [97] [98] [99] [100] [101] 7.4. $D$ is reduced.  [102] [103] [104]
7.5. Equality of $D$ and $C^{red}$.  [105] [106] [107]
7.6. Consequences of the relationship between $D$ and $C$.  [108] [109]
[110] \hbox to\hsize {\hfil {\fam \bffam \tenbf References. }\hfil } 
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[111] [112] [113]
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[][]$[]$\tenrm : Sur les repr^^Sesentations mod-u-laires de degr^^Se $2$ de

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\tensc Department of Math-e-mat-ics, Uni-ver-sity of Cal-i-for-nia at Berke-|

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