Henri Johnston

The Schirokauer map, p-rationality, and applications

For a number field K and a rational prime p, we recall the definition of the Schirokauer map and describe the connection to the so-called p-rationality of K. We then consider applications including (time permitting): (i) the unconditional computation of the unit group of a number field, (ii) the p-rationality of real cyclotomic fields with consequences for p-divisibility of their class numbers and/or (iii) the construction of certain Galois representations with open image. This is joint work with Tommy Hofmann (Siegen).