Foreword to the Special Issues in honor of Andrei Suslin on his 60th birthday

It is a great pleasure for the Editors of the Journal of K-Theory to congratulate their fellow Editor, colleague and friend Andrei Suslin on his 60th birthday and to wish him many more birthdays to come. For this occasion, the Journal of K-Theory is following a tradition begun by the earlier journal K-Theory to honor A. Grothendieck and D. Quillen on their 60th birthdays and is bringing out 2 special issues in honor of Andrei. This is the first issue. The second issue will appear later this year. We are also pleased to announce that the journal Documenta Mathematica will also honor Andrei this year with a volume of its journal. Andrei’s achievements and influence on the development of subjects served by our journal are enormous. We mention just a few of the highlights. His early work in the period 1974–1981 concerned projective, symplectic, and orthogonal modules and their automorphism groups. His solution in 1976 of the Serre conjecture on the freeness of projective modules over a polynomial ring over a field, established independently by Daniel Quillen in the same year, earned him the Komsomol Prize, the most prestigious honor for young scientists in the former Soviet Union. His paper also contained the analogous result for symplectic modules. One does not expect the same result for quadratic modules over a polynomial ring over a field (of characteristic not equal 2), but rather that such modules are extended. This result was proved in a joint paper with his student V.I. Kopeiko in 1977, under the condition that the Witt index of the module is at least 2. All of the above results are closely tied to the cancellation problem for modules over commutative rings and this was the topic of Andrei’s talk at ICM 1978 in Helsinki. It would be the first of 3 ICM talks he was invited to give, the second of which would be a plenary talk. In the years immediately after the Helsinki meeting, his work included the normality of the elementary subgroup of a general linear group of rank at least 3 over a module finite ring (one which is finitely generated as a module over its center), the centrality of any Steinberg group extension of rank at least 4 over a module finite ring (joint with his student M.S. Tulenbaev), and his stability theorem for higher K-groups over rings of finite stable rank. The first and last paper of the current issue use ideas, techniques, and results from the early period above. At the beginning of the 1980s, Andrei turned his attention to the K-theory of fields and division rings. By a classical result of Kummer, the norm residue homomorphism of degree 1 was known to be an isomorphism. In 1982, Andrei showed together with A. Merkurjev that the norm residue homomorphism of degree