Mon, September 14, 2020
Public Access

Category: All

September 2020
Mon Tue Wed Thu Fri Sat Sun
  1 2 3 4 5 6
7 8 9 10 11 12 13
14 15 16 17 18 19 20
21 22 23 24 25 26 27
28 29 30        
3:00pm [3:00pm] Sumit Mishra, Emory University
Date and Time: Monday 14 September, 3:00 p.m - 4.00 p.m. Google Meet Link: Speaker: Sumit Mishra, Emory University Title: Local-global principles for norms over semi-global fields. Abstract: Let K be a complete discretely valued field with the residue field \kappa. Let F be the function field of a smooth, projective, geometrically integral curve over K and \mathcal{X} be a regular proper model of F such that the reduced special fibre X is a union of regular curves with normal crossings. Suppose that the graph associated to \mathcal{X} is a tree (e.g. F = K(t)). Let L/F be a Galois extension of degree n such that n is coprime to \text{char}(\kappa). Suppose that \kappa is an algebraically closed field or a finite field containing a primitive n^{\rm th} root of unity. Then we show that the local-global principle holds for the norm one torus associated to the extension L/F with respect to discrete valuations on F, i.e., an element in F^{\times} is a norm from the extension L/F if and only if it is a norm from the extensions L\otimes_F F_\nu/F_\nu for all discrete valuations \nu of F.

4:00pm [4:00pm] Manish Kumar, ISI Bangalore
Speaker: Manish Kumar, ISI Bangalore Time: Monday 14th September 4 to 5pm (joining time 3.50pm) Google Meet Link: Title: On various conjectures of Abhyankar on the fundamental group and coverings of curves in positive characteristic. Abstract: Abhyankar made many conjectures related to the fundamental group which led to a lot of interesting mathematics. We will discuss some of them and their status in this talk.