| Electronic ISBN: | 978-0-8218-8525-3 |
| Product Code: | MEMO/216/1016.E |
| List Price: | $70.00 |
| MAA Member Price: | $63.00 |
| AMS Member Price: | $42.00 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 216; 2012; 114 ppMSC: Primary 22; 11;
The authors construct new families of smooth admissible \(\overline{\mathbb{F}}_p\)-representations of \(\mathrm{GL}_2(F)\), where \(F\) is a finite extension of \(\mathbb{Q}_p\). When \(F\) is unramified, these representations have the \(\mathrm{GL}_2({\mathcal O}_F)\)-socle predicted by the recent generalizations of Serre's modularity conjecture. The authors' motivation is a hypothetical mod \(p\) Langlands correspondence.
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Table of Contents
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Chapters
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1. Introduction
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2. Representation theory of $\Gamma $ over $\bar {\mathbb F}_p$ I
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3. Representation theory of $\Gamma $ over $\bar {\mathbb F}_p$ II
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4. Representation theory of $\Gamma $ over $\bar {\mathbb F}_p$ III
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5. Results on $K$-extensions
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6. Hecke algebra
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7. Computation of $\mathbb {R}^1\mathcal {I}$ for principal series
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8. Extensions of principal series
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9. General theory of diagrams and representations of ${\mathrm {GL}}_2$
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10. Examples of diagrams
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11. Generic Diamond weights
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12. The unicity Lemma
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13. Generic Diamond diagrams
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14. The representations $D_{0}(\rho )$ and $D_1(\rho )$
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15. Decomposition of generic Diamond diagrams
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16. Generic Diamond diagrams for $f\in \{1,2\}$
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17. The representation $R(\sigma )$
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18. The extension Lemma
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19. Generic Diamond diagrams and representations of ${\mathrm {GL}}_2$
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20. The case $F=\mathbb Q_{p}$
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The authors construct new families of smooth admissible \(\overline{\mathbb{F}}_p\)-representations of \(\mathrm{GL}_2(F)\), where \(F\) is a finite extension of \(\mathbb{Q}_p\). When \(F\) is unramified, these representations have the \(\mathrm{GL}_2({\mathcal O}_F)\)-socle predicted by the recent generalizations of Serre's modularity conjecture. The authors' motivation is a hypothetical mod \(p\) Langlands correspondence.
-
Chapters
-
1. Introduction
-
2. Representation theory of $\Gamma $ over $\bar {\mathbb F}_p$ I
-
3. Representation theory of $\Gamma $ over $\bar {\mathbb F}_p$ II
-
4. Representation theory of $\Gamma $ over $\bar {\mathbb F}_p$ III
-
5. Results on $K$-extensions
-
6. Hecke algebra
-
7. Computation of $\mathbb {R}^1\mathcal {I}$ for principal series
-
8. Extensions of principal series
-
9. General theory of diagrams and representations of ${\mathrm {GL}}_2$
-
10. Examples of diagrams
-
11. Generic Diamond weights
-
12. The unicity Lemma
-
13. Generic Diamond diagrams
-
14. The representations $D_{0}(\rho )$ and $D_1(\rho )$
-
15. Decomposition of generic Diamond diagrams
-
16. Generic Diamond diagrams for $f\in \{1,2\}$
-
17. The representation $R(\sigma )$
-
18. The extension Lemma
-
19. Generic Diamond diagrams and representations of ${\mathrm {GL}}_2$
-
20. The case $F=\mathbb Q_{p}$
