Welcome to the BU number theory expository seminar, Spring 2020!

The topic is: Abhyankar's conjecture

If you have any corrections or additions for this webpage, just email me (Alex).

Time : Monday 11.15am-12.45pm (room is booked till 1.15 for extended discussion, but talks should aim for an hour and a half)
Place : PSY B37 to socially distance we now meet online via Zoom, please contact me if you would like to be added to the mailing list and receive the Zoom links for future weeks.

Seeing as this topic was lovingly stolen from a seminar in Berlin I have copied their plan for now, which we can adjust later to add background and explore topics that interest us.


DateTopic Speaker PlanNotes
27/11. Introduction Alex (show)(notes)
3/22. Ramification of curves John (show)(notes)
10/23. A cohomological interlude Ricky (show)(notes)
18/24. Serre’s proof in the solvable caseAngus (show)(notes)
24/25. Rigid analytic spaces Aash (show)
2/36. Coherent modules and rigid analytic GAGAAash (show)
9/3No seminar; Spring "break" (show)
16/37. Raynaud’s generic fiber John (show)(notes)
23/38. Formal patching Ricky (show)
30/39. Raynaud’s proof I Angus (show)
6/410. Raynaud’s proof II Alex (show)
13/411. Raynaud’s proof II 1/2 Aash (show)
22/412. Raynaud’s proof III Alex (show)(notes)
27/413. Raynaud’s proof IV Angus (show)


[Bos14] S. Bosch, Lectures on Formal and Rigid Geometry, Springer, 2014. Link.

[BLR00] J.-B. Bost, F. Loeser, M. Raynaud, Courbes semi-stables et groupe fondamental en geometrie algebrique, Prog. in Math. 187, Birkhäuser, 2000. Link (readable table of contents).

[Cas16] P. A. Castillejo, Grothendieck-Ogg-Shafarevich formula for ℓ-adic sheaves, Master Thesis (2016). Link.

[Gar14] M. A. Garuti, Rigid Geometry and Galois Extensions of Function Fields in One Variable. Link.

[HOPS14] D. Harbater, A. Obus, R. Pries, K. Stevenson, Abhyankar’s conjectures in Galois theory: Current status and future directions, arXiv:1408.0859 (2014). Link.

[HS99] D. Harbater and K. Stevenson, Patching and thickening problems, J. Alg. 212 (1999), 272– 304. Link.

[Kat86] N. M. Katz, Local-to-global extensions of representations of fundamental groups, Ann. Inst. Fourier 36 (1986), 69–106. Link.

[KR14] Lars Kindler, Kay Rülling Introductory course on ℓ-adic sheaves and their ramification theory on curves. Link.

[Pop95] F. Pop, Étale Galois covers of affine smooth curves, Invent. Math. 120 (1995), 555–578. Link.

[Ray94] M. Raynaud, Revêtements de la droite affine en caractéristique p > 0 et conjecture d’Abhyankar, Invent. Math. 116 (1994), 425–462. Link.

[Ser90] J. -P. Serre, Construction de revêtements étales de la droite affine en caractéristique p, C. R. Acad. Sci. Paris Sér. I Math. 311 (1990), 341–346. Link.

Some previous instances of BUNTES: