Skip to main content

p-adic Variation in Arithmetic Geometry: A Survey

  • 1288 Accesses

Part of the Progress in Mathematics book series (PM,volume 321)

Abstract

The main goal of this survey is to provide a general overview of the theme of p-adic variation, both from a historical and technical view point. We start off with Kummer’s work and Iwasawa’s treatment of cyclotomic fields, which eventually paved the way to the modern p-adic variational techniques. These methods have proved extremely powerful and enabled us to gain access to some of the most important problems in mathematics, such as the Bloch-Kato conjectures and Langlands’ Programme. We will point at a variety of concrete applications in this vein.

Keywords

  • Iwasawa theory
  • Modular motives

Dedicated to the memory of Robert Coleman

Mathematics Subject Classification (2010). 11G05; 11G07; 11G40; 11R23; 14G10.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-3-319-47779-4_1
  • Chapter length: 27 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   89.00
Price excludes VAT (USA)
  • ISBN: 978-3-319-47779-4
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   119.99
Price excludes VAT (USA)
Hardcover Book
USD   119.99
Price excludes VAT (USA)

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Kâzım Büyükboduk .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2017 Springer International Publishing AG

About this chapter

Cite this chapter

Büyükboduk, K. (2017). p-adic Variation in Arithmetic Geometry: A Survey. In: Mourtada, H., Sarıoğlu, C., Soulé, C., Zeytin, A. (eds) Algebraic Geometry and Number Theory . Progress in Mathematics, vol 321. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-47779-4_1

Download citation