# Goro Shimura

Goro Shimura | |
---|---|

Born |
Hamamatsu, Japan | 23 February 1930

Nationality | Japanese |

Fields | Mathematics |

Institutions | Princeton University |

Alma mater | University of Tokyo |

Doctoral students |
Chris Yude Zhao Don Blasius Paul Garrett Melvin Hochster Robert Rumely |

Known for | Modularity theorem |

Notable awards |
Cole Prize (1976) Asahi Prize (1991) Steele Prize (1996) |

**Goro Shimura** (志村 五郎 *Shimura Gorō*, born 23 February 1930) is a Japanese mathematician, and currently a professor emeritus of mathematics (former Michael Henry Strater Chair) at Princeton University.

## Life and career

Shimura was a colleague and a friend of Yutaka Taniyama. They wrote a book (the first book treatment) on the complex multiplication of abelian varieties, an area which in collaboration they had opened up.

Shimura then wrote a long series of major papers, extending the phenomena found in the theory of complex multiplication and modular forms to higher dimensions (amongst other results). This work (and other developments it provoked) provided some of the 'raw data' later incorporated into the Langlands program. It equally brought out the concept, in general, of *Shimura variety*; which is the higher-dimensional equivalent of modular curve. Even to define in general a Shimura variety is quite a formidable task: they bear, roughly speaking, the same relation to general Hodge structures as modular curves do to elliptic curves.

Shimura himself has described his approach as 'phenomenological': his interest is in finding new types of interesting behaviour in the theory of automorphic forms. He also argues for a 'romantic' approach, something he finds lacking in the younger generation of mathematician. The central 'Shimura variety' concept has been tamed (by application of Lie group and algebraic group theory, and the extraction of the concept 'parametrises interesting family of Hodge structures' by reference to the algebraic geometry theory of 'motives', which is still largely conjectural). In that sense his work is now "mainstream-for-Princeton"; but this assimilation (through David Mumford, Pierre Deligne and others) hardly includes all of the content.

He is known to a wider public through the important modularity theorem (previously known as the Taniyama-Shimura conjecture before being proven in the 1990s); Kenneth Ribet has shown that the famous Fermat's last theorem follows from a special case of this theorem. Shimura dryly commented that his first reaction on hearing of Andrew Wiles's proof of the semistable case of the theorem was 'I told you so'.^{[1]}

Among many honors and awards, Shimura received the Cole Prize for number theory in 1976 and the Steele Prize for lifetime achievement in 1996, both from the American Mathematical Society. His *Collected Works* have been published, in five volumes.

His hobbies are shogi problems of extreme length and collecting Imari porcelain. *The Story of Imari: The Symbols and Mysteries of Antique Japanese Porcelain* is a non-fiction work by Shimura published by Ten Speed Press in 2008.

## See also

- Eichler–Shimura congruence relation
- Eichler–Shimura isomorphism
- Shimura correspondence
- Shimura's reciprocity law
- Shimura subgroup
- Shimura variety

## Works

### Mathematical books

- Shimura, Goro; Taniyama, Yutaka (1961),
*Complex multiplication of abelian varieties and its applications to number theory*, Publications of the Mathematical Society of Japan,**6**, Tokyo: The Mathematical Society of Japan, MR 0125113 Later expanded and published as Shimura (1997) - Shimura, Goro (1968).
*Automorphic Functions and Number Theory*. Lecture Notes in Mathematics, Vol. 54 (Paperback ed.). Springer. ISBN 978-3-540-04224-2. - Shimura, Goro (1971-08-01).
*Introduction to the Arithmetic Theory of Automorphic Functions*(Paperback ed.). Princeton University Press. ISBN 978-0-691-08092-5. - It is published from Iwanami Shoten in Japan. - Shimura, Goro (1997-07-01).
*Euler Products and Eisenstein Series*. CBMS Regional Conference Series in Mathematics (Paperback ed.). American Mathematical Society. ISBN 978-0-8218-0574-9. - Shimura, Goro (1997).
*Abelian Varieties with Complex Multiplication and Modular Functions*(Hardcover ed.). Princeton University Press. ISBN 978-0-691-01656-6. An expanded version of Shimura & Taniyama (1961). - Shimura, Goro (2000-08-22).
*Arithmeticity in the Theory of Automorphic Forms*. Mathematical Surveys and Monographs (Paperback ed.). American Mathematical Society. ISBN 978-0-8218-2671-3. - Shimura, Goro (2004-03-01).
*Arithmetic and Analytic Theories of Quadratic Forms and Clifford Groups*. Mathematical Surveys and Monographs (Hardcover ed.). American Mathematical Society. ISBN 978-0-8218-3573-9. - Shimura, Goro (2007).
*Elementary Dirichlet Series and Modular Forms*. Springer Monographs in Mathematics (Hardcover ed.). Springer. ISBN 978-0-387-72473-7.- Shimura, Goro (2009-12-28).
*Elementary Dirichlet Series and Modular Forms*. Springer Monographs in Mathematics (Paperback ed.). Springer New York. ISBN 978-1-4419-2478-0.

- Shimura, Goro (2009-12-28).
- Shimura, Goro (2010-07-15).
*Arithmetic of Quadratic Forms*. Springer Monographs in Mathematics (Hardcover ed.). Springer. ISBN 978-1-4419-1731-7.

### Non-fiction

- Shimura, Goro (2008-06-01).
*The Story of Imari: The Symbols and Mysteries of Antique Japanese Porcelain*(Hardcover ed.). Ten Speed Press. ISBN 978-1-58008-896-1. - Shimura, Goro (2008-09-05).
*The Map of My Life*(Hardcover ed.). Berlin: Springer-Verlag. ISBN 978-0-387-79714-4. MR 2442779.- Shimura, Goro (2009-12-28).
*The Map of My Life*(Paperback ed.). Springer New York. ISBN 978-1-4419-2724-8.

- Shimura, Goro (2009-12-28).

### Collected papers

- Shimura, Goro (2002).
*Collected Papers*. Ⅰ: 1954-1965 (Hardcover ed.). Springer. ISBN 978-0-387-95406-6. - Shimura, Goro (2002).
*Collected Papers*. Ⅱ: 1967-1977 (Hardcover ed.). Springer. ISBN 978-0-387-95416-5. - Shimura, Goro (2003).
*Collected Papers*. Ⅲ: 1978-1988 (Hardcover ed.). Springer. ISBN 978-0-387-95417-2. - Shimura, Goro (2003).
*Collected Papers*. Ⅳ: 1989-2001 (Hardcover ed.). Springer. ISBN 978-0-387-95418-9.

## References

## External links

- O'Connor, John J.; Robertson, Edmund F., "Goro Shimura",
*MacTutor History of Mathematics archive*, University of St Andrews. - Goro Shimura at the Mathematics Genealogy Project