[Search][Subject Index][MathMap][Tour][Help!]

	ABOUT: [Introduction][History][Related areas][Subfields] POINTERS: [Texts][Software][Web links][Selected topics here] 11S Algebraic number theory: local and p-adic fields

Introduction

History

Applications and related fields

The p-adics are formed by completing the rationals with respect to various non-archimedean metrics; thus the material on metric spaces is likely to be relevant.

Subfields

• 11S05: Polynomials
• 11S15: Ramification and extension theory
• 11S20: Galois theory
• 11S23: Integral representations
• 11S25: Galois cohomology, See also 12Gxx, 16H05
• 11S31: Class field theory; p-adic formal groups, See also 14L05
• 11S37: Langlands-Weil conjectures, nonabelian class field theory, See also 11Fxx, 22E50
• 11S40: Zeta functions and L-functions, See also 11M41, 19F27
• 11S45: Algebras and orders, and their zeta functions, See also 11R52, 11R54, 16H05, 16Kxx
• 11S70: K-theory of local fields, See also 19Fxx
• 11S80: Other analytic theory (analogues of beta and gamma functions, p-adic integration, etc.)
• 11S85: Other nonanalytic theory
• 11S90: Prehomogeneous vector spaces [new in 2000]
• 11S99: None of the above but in this section

Parent field: 11: Number Theory

Browse all (old) classifications for this area at the AMS.

Textbooks, reference works, and tutorials

• Iwasawa, Kenkichi, "Local class field theory", The Clarendon Press, Oxford University Press, New York, 1986. 155pp. ISBN 0-19-504030-9
• Gouvêa, Fernando Q.: "p-adic numbers: an introduction", Universitext, Springer-Verlag, Berlin, 1993. 282 pp. ISBN 3-540-56844-1

See also the references for number theory in general.

Software and tables

Other web sites with this focus

Selected topics at this site

• What are the p-adic numbers and how are they relevant to Wiles's proof of Fermat's Last Theorem?
• Examples of sequences of rationals which have different limits in different p-adic completions of Q.
• The p-adic Waring's problem
• Extensions of local fields