Algebraic K-theory is a subject area in mathematics with connections to geometry, topology, ring theory, and number theory. Geometric, algebraic, and arithmetic...

it is a cohomology theory known as topological K-theory. In algebra and algebraic geometry, it is referred to as algebraic K-theory. It is also a fundamental...

Algebraic number theory is a branch of number theory that uses the techniques of abstract algebra to study the integers, rational numbers, and their generalizations...

algebraic number theory. This study reveals hidden structures behind the rational numbers, by using algebraic methods. The notion of algebraic number field...

In algebra, ring theory is the study of rings—algebraic structures in which addition and multiplication are defined and have similar properties to those...

Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems...

In algebraic number theory, an algebraic integer is a complex number that is integral over the integers. That is, an algebraic integer is a complex root...

study higher algebraic K-theory in the special case of fields. It was hoped this would help illuminate the structure for algebraic K-theory and give some...

In mathematics, the equivariant algebraic K-theory is an algebraic K-theory associated to the category Coh G ⁡ ( X ) {\displaystyle \operatorname {Coh}...

In mathematics, there are several theorems basic to algebraic K-theory. Throughout, for simplicity, we assume when an exact category is a subcategory of...

theorem Algebraic K-theory Exact sequence Glossary of algebraic topology Grothendieck topology Higher category theory Higher-dimensional algebra Homological...

algebra, an adelic algebraic group is a semitopological group defined by an algebraic group G over a number field K, and the adele ring A = A(K) of K...

In algebra, the fundamental theorem of algebraic K-theory describes the effects of changing the ring of K-groups from a ring R to R [ t ] {\displaystyle...

resembles topological K-theory more than algebraic K-theory. In particular, a Bott periodicity theorem holds. So there are only two K-groups, namely K0,...

the study of algebraic groups belongs both to algebraic geometry and group theory. Many groups of geometric transformations are algebraic groups; for example...

construction. By definition, K i ( R ) = π i ( K R ) {\displaystyle K_{i}(R)=\pi _{i}(K_{R})} . Dominique Arlettaz, Algebraic K-theory of rings from a topological...

an American-Canadian mathematician known for his contributions to algebraic K-theory and the development of condensed mathematics, in collaboration with...

Suslin, refers to the invariance of mod-n algebraic K-theory under the base change between two algebraically closed fields: Suslin (1983) showed that for...

extension L/K is algebraic if and only if every sub K-algebra of L is a field. The following three properties hold: If E is an algebraic extension of...

ideals, and modules over such rings. Both algebraic geometry and algebraic number theory build on commutative algebra. Prominent examples of commutative rings...

Gabber, Ofer (1992), "K-theory of Henselian local rings and Henselian pairs", Algebraic K-theory, commutative algebra, and algebraic geometry (Santa Margherita...

field K [ T ] {\displaystyle K[T]} . A matroid that can be generated in this way is called an algebraic matroid. No good characterization of algebraic matroids...

In mathematics, topological K-theory is a branch of algebraic topology. It was founded to study vector bundles on topological spaces, by means of ideas...

important for the structure theory of linear algebraic groups. For a linear algebraic group G over an algebraically closed field k, a Borel subgroup of G means...

American mathematician known for his work in differential topology, algebraic K-theory and low-dimensional holomorphic dynamical systems. Milnor is a distinguished...

Derived algebraic geometry is a branch of mathematics that generalizes algebraic geometry to a situation where commutative rings, which provide local charts...

mathematics, algebraic L-theory is the K-theory of quadratic forms; the term was coined by C. T. C. Wall, with L being used as the letter after K. Algebraic L-theory...

Quillen–Lichtenbaum conjecture is a conjecture relating étale cohomology to algebraic K-theory introduced by Quillen (1975, p. 175), who was inspired by earlier...

MR 0298694. Quillen, Daniel (1973). "Higher algebraic K-theory. I". Algebraic K-theory, I: Higher K-theories (Proc. Conf., Battelle Memorial Inst., Seattle...

1 + i {\displaystyle 1+i} is algebraic because it is a root of x4 + 4. All integers and rational numbers are algebraic, as are all roots of integers...