Thời gian: 16h30, thứ năm, 25/07/2024

Tóm tắt: Galois covers in characteristic $p > 0$ exhibit distinct properties compared to those in characteristic $0$. One notable difference is the existence of families of covers with varying ramification data. In this talk, we focus on the moduli space $mathcal{ASW}_{(d_1, d_2, ldots, d_n)}$, which parametrizes $mathbb{Z}/p^n$-covers of the projective line in characteristic $p > 0$ with $mathbb{Z}/p^i$-subcovers possessing conductor $d_i$. In particular, we investigate the geometry of $mathcal{ASW}_{(d_1, d_2, ldots, d_n)}$ by exploring the deformations of cyclic covers, particularly examining changes in the $p$-rank and the number of branch points. Our main tool for analyzing these deformations is the refined Swan conductor, an important invariant from Kato's higher class field theory, which measures how far a Galois cover over a DVR is from having separable reduction.

Hình thức: Offline tại phòng 612 nhà A6 hoặc online qua google meet, link cụ thể https://meet.google.com/yep-kbzk-eao?pli=1&authuser=1