Jürgen Neukirch (24 July 1937 – 5 February 1997) was a German

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

known for his work on algebraic number theory.

Education and career

Neukirch received his diploma in mathematics in 1964 from the

University of Bonn The Rhenish Friedrich Wilhelm University of Bonn (german: Rheinische Friedrich-Wilhelms-Universität Bonn) is a public research university located in Bonn, North Rhine-Westphalia, Germany. It was founded in its present form as the ( en, Rhine ...

. For his Ph.D. thesis, written under the direction of

Wolfgang Krull Wolfgang Krull (26 August 1899 – 12 April 1971) was a German mathematician who made fundamental contributions to commutative algebra, introducing concepts that are now central to the subject. Krull was born and went to school in Baden-Baden. H ...

, he was awarded in 1965 the Felix-Hausdorff-Gedächtnis-Preis. He completed his

habilitation Habilitation is the highest university degree, or the procedure by which it is achieved, in many European countries. The candidate fulfills a university's set criteria of excellence in research, teaching and further education, usually including ...

one year later. From 1967 to 1969 he was guest professor at Queen's University in

Kingston, Ontario Kingston is a city in Ontario, Canada. It is located on the north-eastern end of Lake Ontario, at the beginning of the St. Lawrence River and at the mouth of the Cataraqui River (south end of the Rideau Canal). The city is midway between Toront ...

and at the

Massachusetts Institute of Technology The Massachusetts Institute of Technology (MIT) is a Private university, private Land-grant university, land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern t ...

Cambridge, Massachusetts Cambridge ( ) is a city in Middlesex County, Massachusetts, United States. As part of the Greater Boston, Boston metropolitan area, the cities population of the 2020 United States Census, 2020 U.S. census was 118,403, making it the fourth most ...

, after which he was a professor in Bonn. In 1971 he became a professor at the

University of Regensburg The University of Regensburg (german: link=no, Universität Regensburg) is a public research university located in the medieval city of Regensburg, Bavaria, a city that is listed as a UNESCO World Heritage Site. The university was founded on ...

Contributions

He is known for his work on the embedding problem in algebraic number theory, the Báyer–Neukirch theorem on

special values of L-functions In mathematics, the study of special values of L-functions is a subfield of number theory devoted to generalising formulae such as the Leibniz formula for pi, namely :1 \,-\, \frac \,+\, \frac \,-\, \frac \,+\, \frac \,-\, \cdots \;=\; \frac,\! ...

, arithmetic Riemann existence theorems and the

Neukirch–Uchida theorem In mathematics, the Neukirch–Uchida theorem shows that all problems about algebraic number fields can be reduced to problems about their absolute Galois groups. showed that two algebraic number fields with the same absolute Galois group are isom ...

in birational

anabelian geometry Anabelian geometry is a theory in number theory which describes the way in which the algebraic fundamental group ''G'' of a certain arithmetic variety ''X'', or some related geometric object, can help to restore ''X''. The first results for num ...

. He gave a simple description of the reciprocity maps in local and global class field theory.

Books

Neukirch wrote three books on class field theory, algebraic number theory, and the

cohomology In mathematics, specifically in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups, usually one associated with a topological space, often defined from a cochain complex. Cohomology can be viewe ...

of number fields: * * * *

Notes

External links

*
On Neukirch's death
(in German) * {{DEFAULTSORT:Neukirch, Jurgen 1937 births 1997 deaths 20th-century German mathematicians Number theorists University of Bonn alumni University of Bonn faculty University of Regensburg faculty