In recent years, there has been a growing interest in obstructions to the existence of integral points on varieties. For example, given an extension K/k of number fields of degree n, one might ask when can values of a polynomial P(t) over k be represented by norms of elements of K? In 2012, Colliot-Thelene and Harari asked for a local-global principle for integral points and strong approximation for varieties defined by x^2 - a y^2 = P(t), where P(t) is a separable polynomial of degree at least 3. In this talk, we'll consider families of these generalized affine Chatelet surfaces. Under certain conditions on the Galois group of the polynomial, we will provide an approach for constructing explicit representatives of the Brauer classes for these surfaces. Finally we provide an effective method for computing the Brauer-Manin set using these representatives.
Tuesday, September 13th, at 4:00pm in HBH 227
Return to talks from Fall 2016