Masayoshi Nagata
Masayoshi Nagata | |
|---|---|
 | |
| Born | February 9, 1927 |
| Died | August 27, 2008 (aged 81) Kyoto, Japan |
| 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 |
| Workplaces | Kyoto University |
| Thesis | Research on the 14th problem of Hilbert (1957) |
| Tadasi Nakayama | |
Doctoral students | Shigefumi Mori |
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. He was celebrated for the construction of a number of intricate counterexamples for some seemingly plausible statements in commutative algebra and algebraic geometry, earning him the nickname "Mr. Counterexample".[1]
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.[2]
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
{{citation}}: ISBN / Date incompatibility (help)
References
- ↑ Miyanishi, Masayoshi. "Masayoshi Nagata (1927–2008) and his mathematics" (PDF). Kyoto Journal of Mathematics. 50 (4): 645–659. doi:10.1215/0023608X-2010-008.pdf.
- ↑ I. P. Shestakov, & U. U. Umirbaev (2004) Journal of the American Mathematical Society 17, 197–227.
- 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