Analogue of the Chiodo inequality for the ramification depth in the case of degree p2 extensions

Abstract

In this paper we study the ramification in extensions of complete discrete valuation fields. In the perfect residue field case, there is a classical theory of ramification groups due to J. P. Serre. A. Chiodo introduced the notion of ramification depth, which is close to the classical notion of different. He also obtained an inequality, which pointed out a fundamental relation between the ramification depth in a cyclotomic extension of degree p2 with the ramification depth in a subextension of degree p. In the present paper we focus on the case of the degree p2 extension, which is a composit field of two degree p extensions.