A reading and learning seminar on Perfectoid spaces
Duration: June 4th 2025 to July 2025.
A mini-course on A^1-homotopy theory
For the detailed plan see the webpage.
Talk 1: Introduction, October 24, 2024, 16:00--17:30 (IST) #Auditorium
Talk 2: Representability for torsors and computations, October 29, 2024, 14:30--16:00 (IST) #Auditorium
Talk 3: Basics on model categories and Nisnevich topology, November 5, 2024, 16:00--17:30 (IST) #Auditorium
Talk 4: Homotopy quotients/pushouts, homotopy sheaves of groups, fiber sequences in A^1 homotopy theory, November 7, 2024, 16:00 - 17:30 (IST) #Auditorium
Talk 5: Bigraded spheres and affine/projective bundles, November 12, 2024, 16:00 - 17:30 (IST) #Auditorium
Talk 6: Representability of K-theory, November 14, 2024, 16:00 - 17:30 (IST) #Auditorium
Seminar on 'A^1-homotopy theory'
Venue: The lectures will be held in IISER Pune, Madhava Hall.
Next talk is on Thursday 8th Sept 2022 at 5:30 pm in Room: Madhava Hall, Third floor, main building, IISER Pune.
Seminar on Algebraic spaces and Stacks Notes
Disclaimer: The notes will be updated as the seminar progresses. To those who end up reading them, let me know if there are any mathematical errors. :-)
Venue: The lectures will be held in Madhava Hall or Seminar Room 41 (depending on the availability) (Main building, 3rd Floor, IISER Pune) on Mondays from 3:00 to 4:30 pm.
Plan: The objective is to vaguely follow Laumon- Moret Bailly's book "Champs Algébraiques" as a guideline of results. In addition to that, the goal is to see some important examples and constructions. Here is the list of lectures given in the past and that are coming up.
Lecture 1: Etale descent theory and Algebraic spaces (Rakesh Pawar) (17/02/2022)
Lecture 2: Etale equivalence relation and Algebraic spaces (Rakesh Pawar) (24/02/2022)
Lecture 3: 2-category of S-groupoids (Rakesh Pawar) (3/03/2022)
Lecture 4: S-groupoids, 2-Yoneda Lemma and examples of S-groupoids (Rakesh Pawar) (10/03/2022)
Lecture 5: Stacks in general (examples from differential topology) (Praphulla Kaushik) (14/03/2022)
Lecture 6: Stackification, Examples (Rakesh Pawar) (24/03/2022)
Lecture 7: Construction of Grassmannian schemes (Pavan) (31/03/2022)
Lecture 8: Construction of Hilbert and Quot schemes (Rakesh Pawar) (4/04/2022)
Lecture 9: Algebraic Stacks, Deligne-Mumford stacks, Points on Algebraic stacks and Zariski Topology (Rakesh Pawar) (11/04/2022)
Lecture 10: Algebraic stack of Coherent sheaves and locally free sheaves (Rakesh Pawar) (18/04/2022)