algebraic K-theory
English
editNoun
editalgebraic K-theory (uncountable)
- (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 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
editRelated terms
editTranslations
editK theory studied from the point of view of algebra
|
See also
editFurther reading
edit- 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