Rigid Local Systems and Sporadic Simple Groups

Nicholas Michael Katz, Princeton University, New Jersey, Antonio Rojas-Leon, Universidad de Sevilla, Spain, and Pham Huu Tiep, Rutgers University, Piscataway, New Jersey

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