An introduction to higher dimensional local fields and adeles

Abstract

These notes are an introduction to higher dimensional local fields and higher dimensional adeles. As well as the foundational theory, we summarise the theory of topologies on higher dimensional local fields and higher dimensional local class field theory.

These notes supersede previous introductory texts on the subject by the author

References in corpus (2)

• An explicit approach to residues on and dualizing sheaves of arithmetic surfaces
• Representations of Higher Adelic Groups and Arithmetic

Cited by in corpus (8)

• Higher adeles and non-abelian Riemann-Roch
• Local Beilinson-Tate Operators
• Zeta Functions on Arithmetic Surfaces
• Automorphicity and Mean-Periodicity
• Adelic geometry on arithmetic surfaces I: idelic and adelic interpretation of the Deligne pairing
• Schmid's Formula for Higher Local Fields
• Adelic descent for K-theory
• Localizations of Morava E-theory and deformations of formal groups