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FAQ Policy. The surveys provided can serve as an introduction for them and offer guidance for further study. Show all. Stavrova and A. This theory occurred in early s in the works of Grothendieck, Bass, and MIlnor, later fantastic progress was achieved in the works of Quillen, Suslin, and other classics.

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Algebraic K-theory relates to a ring a new type of invariants, the values of K-functors, that measure to what extend the answers to classical problems of linear algebra differ from the known answers for fields. Vavilov , A.

Ananyevskiy , A. Historically, algebraic geometry occurred as the study of systems of algebraic equations, and the structure of their solutions. Over a field, such solutions form what is known as an algebraic variety. Starting with s, in the context of some classical problems of number theory, and other important applications, one started to systematically study solutions of algebraic systems over arbitrary commutative rings, and related algebraic and geometric structures, such as schemes, motives, algebraic spaces, etc.

Geometric Methods in Algebra and Number Theory (Progress in Mathematics)

Panin , A. Ananyevskiy , M. Bondarko , V. Petrov and A.

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Homological algebra associates with various situations new invariants, such as homology and cohomology groups, etc. The subfield most prominently represented in Saint Petersburg is the ring cohomology, historically closely related to representation theory of finite groups and associative algebras. Among the people working in this field are A. Generalov , M. Antipov and Yu.