An Introduction to Berkovich Spaces

Specialeforsvar ved Guillermo Gachuz Atitlan

Titel: An Introduction to Berkovich Spaces 

Abstract: Berkovich spaces are the analogue of complex manifolds that appear when one replaces complex numbers by general valued fields. The aim of this thesis is to study the geometric structure and properties behind some Berkovich Spaces. We explore how an absolute value over a field K that satises the non-archimedean inequality induces an R-tree structure on some spaces of multiplicative seminorms. This spaces were introduced in the late 1980s by Vladimir Berkovich as a more geometric alternative to the rigid spaces earlier conceived by Tate

Vejleder: Lars H. Halle
Censor:   Anders Nedergaard Jensen, AU