algebraic K-theory

English

Noun

algebraic K-theory (uncountable)

1. (algebraic geometry) K-theory studied from the point of view of algebra.
   • 1999, E. M. Friedlander, “Lecture VII. Beilinson's vision”, in H. Bass, A. O. Kuku, C. Pedrini, editors, Algebraic K-theory And Its Applications, World Scientific, page 61:

     Algebraic cycles are typically studied by imposing one of several equivalence relations. The equivalence relation most relevant for algebraic K-theory is rational equivalence.

   • 2013, Charles A. Weibel, The K-book: An Introduction to Algebraic K-theory, American Mathematical Society, page ix:

     Algebraic K-theory has two components: the classical theory which centers around the Grothendieck group $K_{0}$ of a category and uses explicit algebraic presentations and higher algebraic K-theory which requires topological or homological machinery to define.

   • 2014, Daniel Scott Farley, Ivonne Johanna Ortiz, Algebraic K-theory of Crystallographic Groups, Springer, Lecture Notes in Mathematics 2113, page 1,

     Algebraic K-theory is a branch of algebra dealing with linear algebra over a general ring R instead of a field. […] Algebraic K-theory plays an important part in many areas of mathematics, especially number theory, algebraic topology and algebraic geometry.

Derived terms

• higher algebraic K-theory

Related terms

• K-theory
• topological K-theory

Translations

K theory studied from the point of view of algebra

• French: K-théorie algébrique f
• German: algebraische K-Theorie f

See also

• K-group

Further reading

• Grothendieck–Riemann–Roch theorem on Wikipedia.Wikipedia
• Grothendieck group on Wikipedia.Wikipedia
• Algebraic K-theory on Encyclopedia of Mathematics
• K-theory on Encyclopedia of Mathematics
• K-functor on Encyclopedia of Mathematics
• Grothendieck group on Encyclopedia of Mathematics
• algebraic K-theory on n-Lab