Oberseminar WiSe 26/27
Die Vorträge finden donnerstags um 16:45 Uhr in Raum WSC-N-U-3.05 im Mathematikgebäude statt. Die Vorträge dauern 60 Minuten. Der Tee findet ab 16:15 Uhr in Raum O-3.46 statt. Alle Interessenten sind herzlich eingeladen!
The seminar takes place on Thursdays in Room WSC-N-U-3.05 in the Math Building , starting at 4:45pm. The duration of each talk is 60 minutes. Before the talks, there is tea in room O-3.46 at 4:15pm. Everybody who is interested is welcome to join!
Directions from the train station.
| 15.10.2026 | Julian Feuerpfeil (Milan/Besançon) | The Tame Fontaine-Mazur Conjecture, Linking Diagrams and Bockstein Spectral Sequences |
| 22.10.2026 | 14-18h Colloquium on the occasion of Georg Hein’s 60th birthday | |
| 29.10.2026 | Alex Küronya (?) | |
| 05.11.2026 | ||
| 12.11.2026 | ||
| 19.11.2026 | ||
| 26.11.2026 | ||
| 03.12.2026 | Elsa Maneval (EPFL) | |
| 10.12.2026 | ||
| 17.12.2026 | ||
| 07.01.2027 | Tamás Szamuely (Pisa) | tba |
| 14.01.2027 | Frank Neumann (Pavia) | tba |
| 21.01.2027 | ||
| 28.01.2027 | ||
| 04.02.2027 |
Abstracts
Julian Feuerpfeil: The Tame Fontaine-Mazur Conjecture, Linking Diagrams and Bockstein Spectral Sequences
The Fontaine-Mazur Conjecture predicts that certain $p$-adic Galois representations of a number field should arise from geometry. In the tame case, i.e., when the representation is only ramified at finitely many places and unramified at the $p$-adic ones, it implies that the image should be finite. In particular, if $G_{K,S}$ denotes the maximal pro-$p$ extension of a number field $K$ unramified outside a finite set $S$ of tame places, then $G_{K,S}$ should admit no nontrivial uniform quotient.
In this talk, after introducing this connection between $p$-adic Galois representations and pro-$p$ Galois groups, we develop a new approach to the latter problem using linking diagrams, Bockstein spectral sequences, and $\mathbb Z_p$-Lie algebras. Linking diagrams encode the presentations of the groups $G_{K,S}$ in a combinatorial way, while the Lie algebras serve as a linearization of potential uniform quotients. The first Bockstein differential recovers the mod-$p$ relations used in an earlier approach by J. Labute (2014), while higher Bockstein differentials yield additional congruences modulo higher powers of $p$. This allows us to remove Labute’s restriction that $p^2\nmid N(\mathfrak{q})-1$ for $\mathfrak{q}\in S$ and, together with a recent equidistribution result for linking diagrams, leads to the observation that $G_{\mathbb{Q},S}$ has no nontrivial uniform quotients with ‘‘probability’‘ at least $1-O(p^{-3})$ for $|S|=3$.