In Spring 2026, Ramanujan Srihari and I are organising a learning seminar on alterations. Please email me or Ramanujan to be added to the mailing list.
Location: Thursdays 2-3:30 pm, APM B412
Goal
The goal of this seminar is to understand the proof of Theorem 4.1 in de Jong's paper [dJ1] (see the references for abbreviations). We will follow the notes [CFL].
Time remaining, we will move onto modern applications and refinements, depending on audience interest.
Schedule
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April 2: Introduction, overview of the proof and basic reductions. Sections 1, 2 and 3 [CFL] (Shubhankar)
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April 9: Constructing good curve fibrations. Sections 4 and 5 [CFL] (Ramanujan)
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April 16: Finding enough multisections of curve fibrations. Sections 6 and 7 [CFL] (Shubhankar)
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April 23: Stable curves. Section 8 [CFL] (Shubhankar)
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April 30: Moduli of stable curves. Section 9 [CFL] (Gavin)
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May 7: Applications of moduli stacks. Section 10 [CFL] (Ramanujan)
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May 14: Semistable curves over discrete valuation rings. Section 11 [CFL] (Poornima)
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May 21: Resolving semistable curves over a regular base. Section 12 [CFL] (Dimitri)
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May 28: Applications (Matt). Note that this talk will be at a different time which is tba.
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June 4: Finiteness of rigid cohomology via alterations (Kiran)
Main reference for the seminar
References
Complementary references
Here are some other references which may be useful to speakers.