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Rigid Local Systems and Sporadic Simple Groups
 
Nicholas Michael Katz Princeton University, Princeton, New Jersey
Antonio Rojas-León Universidad de Sevilla, Sevilla, Spain
Pham Huu Tiep Rutgers University, Piscataway, New Jersey
Softcover ISBN:  978-1-4704-7342-6
Product Code:  MEMO/308/1559
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Not yet published - Preorder Now!
Expected availability date: June 04, 2025
eBook ISBN:  978-1-4704-8146-9
Product Code:  MEMO/308/1559.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Softcover ISBN:  978-1-4704-7342-6
eBook: ISBN:  978-1-4704-8146-9
Product Code:  MEMO/308/1559.B
List Price: $170.00 $127.50
MAA Member Price: $153.00 $114.75
AMS Member Price: $136.00 $102.00
Not yet published - Preorder Now!
Expected availability date: June 04, 2025
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Rigid Local Systems and Sporadic Simple Groups
Nicholas Michael Katz Princeton University, Princeton, New Jersey
Antonio Rojas-León Universidad de Sevilla, Sevilla, Spain
Pham Huu Tiep Rutgers University, Piscataway, New Jersey
Softcover ISBN:  978-1-4704-7342-6
Product Code:  MEMO/308/1559
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Not yet published - Preorder Now!
Expected availability date: June 04, 2025
eBook ISBN:  978-1-4704-8146-9
Product Code:  MEMO/308/1559.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Softcover ISBN:  978-1-4704-7342-6
eBook ISBN:  978-1-4704-8146-9
Product Code:  MEMO/308/1559.B
List Price: $170.00 $127.50
MAA Member Price: $153.00 $114.75
AMS Member Price: $136.00 $102.00
Not yet published - Preorder Now!
Expected availability date: June 04, 2025
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 3082025; 185 pp
    MSC: Primary 11; Secondary 20

    View the abstract.

  • Table of Contents
     
     
    • Chapters
    • 1. Introduction
    • 2. Almost quasisimple groups containing elements with simple spectra
    • 3. Preliminary results on condition $\mathrm {({\bf S+})}$
    • 4. $G_\mathrm {geom}$ and $G_\mathrm {arith}$
    • 5. Structure of $G_\mathrm {geom}$
    • 6. Rationality, moments, and reduction mod $\ell $ of hypergeometric sheaves
    • 7. Descents of hypergeometric sheaves
    • 8. The notational scheme for descents
    • 9. Proving finiteness of $G_\mathrm {geom}$
    • 10. The alternating group $\mathsf {A}_6$
    • 11. The alternating group $\mathsf {A}_7$
    • 12. The Mathieu group $\mathrm {M}_{11}$
    • 13. The Mathieu group ${\mathrm M}_{22}$
    • 14. The Mathieu group $\mathrm {M}_{23}$
    • 15. The Mathieu group $\mathrm {M}_{24}$
    • 16. The MacLaughlin group $\mathrm {McL}$
    • 17. The Janko group $\mathrm {J}_2$
    • 18. The Janko group $\mathrm {J}_3$
    • 19. The Rudvalis group $\mathrm {Ru}$
    • 20. The special linear group $\mathrm {PSL}_3(4)$
    • 21. The special unitary group $\mathrm {PSU}_4(3)$
    • 22. The symplectic group $\mathrm {Sp}_6(2)$
    • 23. The orthogonal group $\Omega ^+_8(2)$
    • 24. The exceptional group $G_2(3)$
    • 25. The exceptional group $G_2(4)$ and its subgroup $\mathrm {SU}_3(4)$
    • 26. The “exceptional” group $\mathrm {SU}_3(3) \cdot 2 \cong G_2(2)$
    • 27. The Suzuki group ${}^2\! B_2(8)$
    • 28. The “exceptional” group $\mathrm {SL}_2(8) \cdot 3 \cong {}^2\! G_2(3)$
    • 29. The Conway group $\mathrm {Co}_1$ and the Suzuki group $\mathrm {Suz}$
    • 30. Complex reflection groups
    • 31. Further local systems for $\mathrm {Sp}_6(2)$, $\mathrm {SU}_3(3)$, ${}^2\! G_2(3)$, and $2\mathsf {A}_7$
    • 32. Further multi-parameter local systems
  • Additional Material
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 3082025; 185 pp
MSC: Primary 11; Secondary 20

View the abstract.

  • Chapters
  • 1. Introduction
  • 2. Almost quasisimple groups containing elements with simple spectra
  • 3. Preliminary results on condition $\mathrm {({\bf S+})}$
  • 4. $G_\mathrm {geom}$ and $G_\mathrm {arith}$
  • 5. Structure of $G_\mathrm {geom}$
  • 6. Rationality, moments, and reduction mod $\ell $ of hypergeometric sheaves
  • 7. Descents of hypergeometric sheaves
  • 8. The notational scheme for descents
  • 9. Proving finiteness of $G_\mathrm {geom}$
  • 10. The alternating group $\mathsf {A}_6$
  • 11. The alternating group $\mathsf {A}_7$
  • 12. The Mathieu group $\mathrm {M}_{11}$
  • 13. The Mathieu group ${\mathrm M}_{22}$
  • 14. The Mathieu group $\mathrm {M}_{23}$
  • 15. The Mathieu group $\mathrm {M}_{24}$
  • 16. The MacLaughlin group $\mathrm {McL}$
  • 17. The Janko group $\mathrm {J}_2$
  • 18. The Janko group $\mathrm {J}_3$
  • 19. The Rudvalis group $\mathrm {Ru}$
  • 20. The special linear group $\mathrm {PSL}_3(4)$
  • 21. The special unitary group $\mathrm {PSU}_4(3)$
  • 22. The symplectic group $\mathrm {Sp}_6(2)$
  • 23. The orthogonal group $\Omega ^+_8(2)$
  • 24. The exceptional group $G_2(3)$
  • 25. The exceptional group $G_2(4)$ and its subgroup $\mathrm {SU}_3(4)$
  • 26. The “exceptional” group $\mathrm {SU}_3(3) \cdot 2 \cong G_2(2)$
  • 27. The Suzuki group ${}^2\! B_2(8)$
  • 28. The “exceptional” group $\mathrm {SL}_2(8) \cdot 3 \cong {}^2\! G_2(3)$
  • 29. The Conway group $\mathrm {Co}_1$ and the Suzuki group $\mathrm {Suz}$
  • 30. Complex reflection groups
  • 31. Further local systems for $\mathrm {Sp}_6(2)$, $\mathrm {SU}_3(3)$, ${}^2\! G_2(3)$, and $2\mathsf {A}_7$
  • 32. Further multi-parameter local systems
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
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