Galois groups over the rationals with ramification constraints
Báo cáo viên: Prof. J. Sonn (Dept. Math., Israel Inst. Technology)

Thời gian: 9h, Thứ 4, Ngày 23/1/2019.
Địa điểm: Phòng 612 Tòa A6 Viện Toán học
Tóm tắt: The inverse Galois problem over the rationals has inspired several variants over time. In this talk, following an introduction to the classical problem and the basic notions involved, we will briefly review the variant which asks for the fewest possible ramified primes in a Galois realization of a finite group over the rationals Q, and then spend most of the remaining talk on a recent variant that asks for Galois realizations of a finite group G over Q in which all the nontrivial inertia subgroups have order two. The only groups for which this can happen are those generated by elements of order two, for example finite nonabelian simple groups. If such a group G has a "regular" realization over the rational function field Q(t), as the splitting field of a polynomial f(t,x), then there are computable conditions on the polynomial which guarantee the existence of infinitely many specializations of t into Q which yield realizations over Q with all inertia groups of order two. As examples, three finite simple groups will be given, together with corresponding polynomials. One application of this result is to unramified realizations of these groups over quadratic fields. Another application is to the problem which motivated this result (time permitting). Joint work with Joachim Koenig and Daniel Rabayev.

Trở lại

19/11/19, Hội nghị, hội thảo:
The IMH School Introduction to Algebraic Schemes and Cohomology
22/11/19, Bài giảng viện:
Berkovich spaces over Z and convergent arithmetic power series
02/12/19, Hội nghị, hội thảo:
04/12/19, Hội nghị, hội thảo:
Hội nghị Đại số-Lý thuyết số-Hình học và Tô pô 2019
09/12/19, Hội nghị, hội thảo:
Workshop Quốc tế về Hình học và Tổ hợp
13/12/19, Bài giảng viện:
How to escape the curse of dimensionality in combinatorics
20/12/19, Bài giảng viện:
Algebraic surfaces with minimal Betti numbers
17/02/20, Hội nghị, hội thảo:
SEAMS school “Arithmetic, Geometry and Model Theory”
04/03/20, Hội nghị, hội thảo:
MIS-IMH research school on Mathematics of Data

Công bố khoa học mới