TWO-DIMENSIONAL LOCAL FIELDS: A STUDY AND FUNCTIONAL ANALYSIS

The neighborhood field related to each point on the twist is utilized to portray a ring of adeles for the twist in the assessment of class field hypothesis of logarithmic bends. This ring gives the space to a correspondence blueprint of the curve's worldwide field of capacities. We broaden this methodology in this review to manage the instance of a logarithmic surface over a restricted field, utilizing correspondence maps for higher nearby fields in a manner similar to the classical case.