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Algebraic K-theory is a branch of mathematics that studies certain groups associated with geometric, algebraic, and arithmetic objects. These groups, called K-groups, are abelian groups that encode information about the original object. Algebraic K-theory is a powerful tool that has been used to solve a wide variety of problems in many areas of mathematics.
The origins of algebraic K-theory can be traced back to the work of Alexander Grothendieck in the 1950s. Grothendieck was interested in developing a theory of higher-dimensional cohomology that would be analogous to classical cohomology theory. In the process, he developed a new approach to the study of vector bundles, which led to the definition of K-theory.
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