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The mathematics of Andrei Suslin. (English) Zbl 1447.20015

From the Introduction: “Andrei Suslin (1950–2018) was both friend and mentor to us. This article discusses some of his many mathematical achievements, focusing on the role he played in shaping aspects of algebra and algebraic geometry. We mention some of the many important results Andrei proved in his career […] Andrei was deeply involved in both the formulation and the solution of many of the most important questions in algebraic \(K\)-theory. […] Towards the end of his career Andrei made important contributions to the modular representation theory of finite group schemes. […] Time and again, Andrei introduced new techniques and structures in order to solve challenging problems […].”
The authors explain contributions of Andrei Suslin to the following topics: projective modules; \(K_2\) of fields and the Brauer group; Milnor \(K\)-theory versus algebraic K-theory; \(K\)-theory and cohomology theories; motivic cohomology and K-theories; modular representation theory.
In each case, there is a helpful description of the context.

MSC:

20G05 Representation theory for linear algebraic groups
20C20 Modular representations and characters
20G10 Cohomology theory for linear algebraic groups
20-03 History of group theory
19-03 History of \(K\)-theory
14-03 History of algebraic geometry
01A60 History of mathematics in the 20th century
14C35 Applications of methods of algebraic \(K\)-theory in algebraic geometry
14F42 Motivic cohomology; motivic homotopy theory
01A70 Biographies, obituaries, personalia, bibliographies

Biographic References:

Suslin, Andrei
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