Nationality Japanese Role Mathematician Institutions Kyoto University Education Nagoya University | Alma mater Nagoya University Fields Mathematics Name Masayoshi Nagata | |
Born February 9, 1927
Obu, Aichi, Japan ( 1927-02-09 ) Doctoral students Shuzo Izumi
Shigefumi Mori Known for Nagata ring
Nagata–Biran conjecture Died August 27, 2008, Kyoto, Kyoto Prefecture, Japan Books Local Rings, Theory of commutative fields, Polynomial rings and affine spaces, On flat extensions of a ring, Field Theory People also search for Hideyuki Matsumura, Shigefumi Mori, Thomas Banchoff | ||
Doctoral advisor Tadashi Nakayama | ||
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.
Nagata's compactification theorem shows that varieties can be embedded in complete varieties. The Chevalley–Iwahori–Nagata theorem describes the quotient of a variety by a group.
He found counterexamples to several open mathematical questions. 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.