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Towards a Modulo $p$ Langlands Correspondence for GL$_2$
 
Christophe Breuil CNRS, Bures-sur-Yvette, France and IHES, Bures-sur-Yvette, France
Vytautas Paškūnas Universität Bielefeld, Bielefeld, Germany
Front Cover for Towards a Modulo $p$ Langlands Correspondence for GL$_2$
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Electronic ISBN: 978-0-8218-8525-3
Product Code: MEMO/216/1016.E
114 pp 
List Price: $70.00
MAA Member Price: $63.00
AMS Member Price: $42.00
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Towards a Modulo $p$ Langlands Correspondence for GL$_2$
Christophe Breuil CNRS, Bures-sur-Yvette, France and IHES, Bures-sur-Yvette, France
Vytautas Paškūnas Universität Bielefeld, Bielefeld, Germany
Available Formats:
Electronic ISBN:  978-0-8218-8525-3
Product Code:  MEMO/216/1016.E
114 pp 
List Price: $70.00
MAA Member Price: $63.00
AMS Member Price: $42.00
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 2162012
    MSC: 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.

  • Table of Contents
     
     
    • 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 $F=\mathbb Q_{p}$
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Volume: 2162012
MSC: 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.

  • 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 $F=\mathbb Q_{p}$
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