## Number Theory Seminar:Dong Quan Nguyen

- Date: 10/25/2012

Speaker(s):
Dong Quan Nguyen: UBC

Location:

University of British Columbia

Description:

We show that for each prime *p* congruent to 1 (mod 8), there exists a threefold *Xp* such that the existence of certain rational points on *Xp* produces

families of generalized Mordell curves and of generalized Fermat curves

that are counterexamples to the Hasse principle explained by the

Brauer–Manin obstruction. We also introduce a notion of the descending

chain condition (DCC) for sequences of curves, and prove that there are

sequences of generalized Mordell curves and of generalized Fermat curves

satisfying DCC.

Other Information:

Location: ESB 2012