Alladi Ramakrishnan Hall

Primitive p-extensions of p-fields

Chandan Singh Dalawat

Harish chandra Institute

It is a fundamental open problem in number theory to classify
all finite extensions of a given number field. As a preliminary, one
should classify all finite extensions of p-fields (completions of number
fields at various primes). Every finite extension is a succession of
primitive extensions (having no intermediate extensions). The only
interesting primitive extensions of a p-field are the p-extensions (whose
degree is a power of p). We will give a natural parametrisation of the
set of primitive p-extensions of a given p-field and show how various
properties of the extension (such as its discriminant) can be read off from
its parameter.