K-theory

 

 

major results

• Norm residue isomorphism theorem
  • isomorphism from Milnor K-theory mod l to étale cohomology
  • Bloch–Kato conjecture
  • generalization of the Milnor conjecture
  • consequence : Quillen–Lichtenbaum conjecture

 

Borel

• Borel's regulator

 

 

topics

• Steinberg symbol
• K-theory
  • Bloch group
    
  • Bloch-Beilinson conjecture
    
  • Borel's regulator
    
  • Periods and transcendental number theory
    
  • regulator
    
  • Zagier's conjecture
    

 

 

 

related items

• topology and vector bundles

 

encyclopedia

• http://en.wikipedia.org/wiki/Algebraic_K-theory
• http://en.wikipedia.org/wiki/K-theory

books

• Charles Weibel, The K-book: An introduction to algebraic K-theory
• Algebra, K-theory, groups, and education

expositions

• CHRISTOPHE SOULE, HIGHER K-THEORY OF ALGEBRAIC INTEGERS AND THE COHOMOLOGY OF ARITHMETIC GROUPS
• Algebraic K-theory of number fields (after A. Borel)
• an introduction to algebraic K-theory
  
  • T. Y. Lam and M. K. Siu, The American Mathematical Monthly, Vol. 82, No. 4 (Apr., 1975), pp. 329-364
• K-THEORY. An elementary introduction
  
  • Max Karoubi. Conference at the Clay Mathematics Research Academy
• The development of Algebraic K-theory before 1980
  
  • Charles A. Weibel
• A brief glance at K-theory
• A BRIEF GUIDE TO ORDINARY K-THEORY

 

 

questions

• http://mathoverflow.net/questions/364/motivation-for-algebraic-k-theory