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...

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

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

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...

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

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,...

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...

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

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

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...

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

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

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

Steenrod algebra Bott periodicity theorem K-theory Topological K-theory Adams operation Algebraic K-theory Whitehead torsion Twisted K-theory Cobordism...

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...

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...

natural numbers k, is a cohomology operation in topological K-theory, or any allied operation in algebraic K-theory or other types of algebraic construction...

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

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

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

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...

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...

mathematics, an algebraic cycle on an algebraic variety V is a formal linear combination of subvarieties of V. These are the part of the algebraic topology of...

In abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known...

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...

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

"for contributions to algebraic topology, particularly equivariant stable homotopy theory, algebraic K-theory, and applied algebraic topology". In 2008,...