O completamento de corpos de números e extensões suavemente ramificadas

Abstract

In this work, we studied the number fields, which are finite extensions of the field of rational numbers. In the first part of the work we did a brief review of basic concepts of Commutative Algebra. Then, we studied the rings of integers in these fields and the unique factorization of its ideals. At last, we have the main subjects of this text, the completions of number fields with respect of an absolute value and the tame ramifications in extensions of henselian fields.