Speaker: Sumit Chandra Mishra, Department of Mathematics, IIT Indore

Host: Sandip Singh

Title: Ruled residue theorem for function fields

Time, day and date: 4:00 PM - 5:00:00 PM, Tuesday, October 07

Venue: Room No. 215, Mathematics Department

Abstract: Let E be a field with a valuation v. In 1983, Ohm proved that for any extension of v to the rational function field E(X)  in one variable, the corresponding residue field extension is either algebraic or ruled, i.e., it is the rational function field in one variable over a finite extension of the residue field of E. This is called the Ruled Residue Theorem. More generally, one can consider the function field F of a curve over E and ask if for all extensions of v to F, the corresponding residue field extension is either algebraic or ruled? If not, is there any bound on the number of extensions of v to F where this fails? I will mention known results for the function fields of conics. Later on, I will discuss the case of function fields of elliptic curves and hyperelliptic curves( joint work with Prof. Karim J. Becher and Dr. Parul Gupta, and joint work with Dr Parul Gupta, respectively).

All are welcome to attend the seminar.