Theoretical Statistics and Mathematics Unit, ISI Delhi

October 23, 2013 (Wednesday) ,
3:30 PM at Webinar

Speaker:
Barinder Banwait,
University of Warwick, UK

Title:
The local to global question in number theory

Abstract of Talk

If a polynomial over the integers is reducible, then clearly so too are all reductions mod p of the polynomial also reducible. But what about the converse...if all of its reductions are reducible, must it reduce over the integers? This is a basic example of a local to global question in number theory, and its answer, like lots of other local to global questions in number theory, is "No". Then challenge then is to understand for which polynomials this converse holds - this is explained by Galois Theory. I will discuss my recent work of studying an analogous local to global problem, replacing "polynomials" with "elliptic curves over number fields", and "reducible" by "possessing an isogeny of prime degree", and trying to explain precisely under which conditions the converse does hold.