Event Type:

Number Theory Seminar

Date/Time:

Tuesday, February 28, 2017 - 16:00 to 17:00

Location:

Bexell 417

Guest Speaker:

Institution:

University of Texas

Abstract:

Let k be an algebraic number field which is a Galois

extension of the rational field. A Minkowski unit in k is

a unit with the additional property that its conjugates under

the Galois action generate a subgroup of units with maximum

possible rank. Minkowski proved long ago that such units always

exist. I will outline a new proof that establishes the existence

of a Minkowski unit \beta such that the Weil height of \beta

is comparable to the sum of the heights of a basis for the

group of units.

If time permits I will describe an analogous but more

difficult result for relative units. This is joint work with

Shabnam Akhtari that appeared recently in the European Journal

of Mathematics.