Rigid Local Systems and Sporadic Simple Groups

Nicholas Michael Katz, Antonio Rojas-Leon, Pham Huu Tiep (Autoren)

Buch | Softcover

185 Seiten

2025
American Mathematical Society (Verlag)
978-1-4704-7342-6 (ISBN)

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Scholarly monographs in pure and applied mathematics compile extended collections of related studies into detailed volumes. Each work is rigorously peer-reviewed under the AMS editorial committee, ensuring high standards and in-depth inquiry across diverse mathematical disciplines.

The Memoirs of the AMS is devoted to the publication of new research in all areas of pure and applied mathematics. The Memoirs is designed particularly to publish long papers of groups of cognate papers in book form, and is under the supervision of the Editorial Committee of the AMS journal Transactions of the American Mathematical Society. All papers are peer-reviewed.

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

Erscheinungsdatum	02.07.2025
Reihe/Serie	Memoirs of the American Mathematical Society
Verlagsort	Providence
Sprache	englisch
Maße	178 x 254 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
ISBN-10	1-4704-7342-9 / 1470473429
ISBN-13	978-1-4704-7342-6 / 9781470473426
Zustand	Neuware