Learning seminar on the work of Friedlander-Suslin ☰

About

In this online learning seminar running in the summer and fall of 2021, we will study the 1997 work of Friedlander and Suslin on strict polynomial functors and finite generation of cohomology of finite group schemes [FS]. Following this, we may explore related works on the proof of finite generation of cohomology rings in other situations, such as in [D]. For background on finite group schemes, see [W].

  • Time and location: Tuesdays, 5-7 Eastern US time, on Zoom.
  • Organizers: Pavel Etingof (MIT), Kent Vashaw (LSU and MIT).

Schedule and notes

  • July 20, 2021: Introduction and Section 1 of [FS], Kent Vashaw. Video part 1. Video part 2. Notes .
  • July 27, 2021: Continuation of Section 1 of [FS], Kent Vashaw. Video. Notes.
  • August 3, 2021: Completion of Section 1 of [FS], Kent Vashaw. Section 2 of [FS], Kevin Coulembier. Video. Notes for part 1. Notes for part 2.
  • August 10, 2021: Section 3 of [FS], Bregje Pauwels. Video. Notes.
  • August 17, 2021: Section 4 of [FS], Bregje Pauwels. Video. Notes. Cheat sheet.
  • August 24, 2021: Completion of Section 4 of [FS], Arun Kannan. Video. Notes.
  • August 31, 2021: Section 5 of [FS], Hongdi Huang. Video. Notes.
  • September 7, 2021: Section 6 of [FS], Victor Ostrik. Video. Notes.
  • September 14, 2021: Introduction to [D1] and [D2], Christopher Drupieski. Video. Notes outline. Notes.
  • September 21, 2021: Completion of introduction to [D1] and [D2], Christopher Drupieski. Video. Notes outline. Notes.
  • September 28, 2021: Skip week- no seminar.
  • October 5, 2021: Section 3 of [D1], Kent Vashaw. Video part 1. Video part 2. Video part 3. Notes.
  • October 12, 2021: Skip week- no seminar.
  • October 19, 2021: Superpolynomial functors and Schur superalgebras, after J. Axtell [A]. Pavel Etingof. Video. Notes.
  • October 26, 2021: Skip week- no seminar.
  • November 2, 2021: Skip week- no seminar.
  • November 9, 2021: Continuation of superpolynomial functors and Schur superalgebras, after J. Axtell [A]. Pavel Etingof. Video.

References

  • [A]: J. Axtell, Spin polynomial functors and representations of Schur superalgebras, Represent. Theory 17 (2013), 584–609.
  • [D1]: C. M. Drupieski, Cohomological finite generation for restricted Lie superalgebras and finite supergroup schemes, Represent. Theory 17 (2013), 469–507.
  • [D2]: C. M. Drupieski, Cohomological finite-generation for finite supergroup schemes, Adv. Math. 288 (2016), 1360–1432.
  • [FS]: E. M. Friedlander and A. Suslin, Cohomology of finite group schemes over a field, Invent. Math. 127 (1997), no. 2, 209–270.
  • [W]: W. C. Waterhouse, Introduction to affine group schemes, Graduate Texts in Mathematics, 66. Springer-Verlag, New York-Berlin, 1979. xi+164 pp.