On Mazur's Dimension Conjecture for Global Deformation Rings
Time: 2026-07-08
Published By: He Liu
Speaker(s): Xinyao Zhang (University of Tokyo)
Time: 14:00-15:00 July 14, 2026
Venue: Lecture Hall, Jiayibing Building, Jingchunyuan 82, BICMR
Mazur’s dimension conjecture predicts that global deformation rings should have the expected Krull dimension dictated by the global characteristic formula. In this talk, I will discuss this conjecture for two-dimensional unrestricted deformation rings over G_{\mathbb Q}. The proof combines a local input from Paškūnas theory with global inputs such as a finiteness result between deformation rings and the Fontaine–Mazur conjecture. If time permits, I will also explain an analogous result in the residually reducible setting.
