Masayoshi Nagata

Masayoshi Nagata (Japanese: 永田 雅宜 Nagata Masayoshi; February 9, 1927 – August 27, 2008) was a Japanese mathematician, known for his work in the field of commutative algebra.

Masayoshi Nagata
Born	(1927-02-09)February 9, 1927 Ōbu, Aichi, Japan
Died	August 27, 2008(2008-08-27) (aged 81) Kyoto, Japan
Nationality	Japanese
Alma mater	Nagoya University
Known for	Nagata ring Nagata's conjecture Nagata's conjecture on curves Nagata's compactification theorem Chevalley–Iwahori–Nagata theorem Zariski–Nagata purity Mori–Nagata theorem Analytically irreducible ring
Scientific career
Fields	Mathematics
Institutions	Kyoto University
Thesis	Research on the 14th problem of Hilbert  (1957)
Doctoral advisor	Tadasi Nakayama
Doctoral students	Shigefumi Mori

Work

Nagata's compactification theorem shows that algebraic varieties can be embedded in complete varieties. The Chevalley–Iwahori–Nagata theorem describes the quotient of a variety by a group.

In 1959, he introduced a counterexample to the general case of Hilbert's fourteenth problem on invariant theory. His 1962 book on local rings contains several other counterexamples he found, such as a commutative Noetherian ring that is not catenary, and a commutative Noetherian ring of infinite dimension.

Nagata's conjecture on curves concerns the minimum degree of a plane curve specified to have given multiplicities at given points; see also Seshadri constant. Nagata's conjecture on automorphisms concerns the existence of wild automorphisms of polynomial algebras in three variables. Recent work has solved this latter problem in the affirmative.

Selected works

• Nagata, Masayoshi (1960), "On the fourteenth problem of Hilbert", Proc. Internat. Congress Math. 1958, Cambridge University Press, pp. 459–462, MR 0116056, archived from the original on 2011-07-17
• Nagata, Masayoshi (1965), Lectures on the fourteenth problem of Hilbert (PDF), Tata Institute of Fundamental Research Lectures on Mathematics, vol. 31, Bombay: Tata Institute of Fundamental Research, MR 0215828
• Nagata, Masayoshi (1962), Local rings, Interscience Tracts in Pure and Applied Mathematics, vol. 13, New York-London: Interscience Publishers a division of John Wiley & Sons, ISBN 0-88275-228-6, MR 0155856

References

• Maruyama, Masaki; Masayoshi Miyanishi; Shigefumi Mori; Tadao Oda (January 2009). "Masayoshi Nagata (1927–2008)" (PDF). Notices of the American Mathematical Society. 56 (1): 58. Retrieved 2008-12-30.
• O'Connor, John J.; Robertson, Edmund F., "Masayoshi Nagata", MacTutor History of Mathematics Archive, University of St Andrews
• Masayoshi Nagata at the Mathematics Genealogy Project