zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
On the history of Hilbert’s twelfth problem: a comedy of errors. (English) Zbl 1044.01530
Material on the history of mathematics in the 20th century. Proceedings of the colloquium to the memory of Jean Dieudonné, Nice, France, January 1996. Marseille: Société Mathématique de France (ISBN 2-85629-065-5/pbk). Sémin. Congr. 3, 243-273 (1998).
Summary: Hilbert’s 12th problem conjectures that one might be able to generate all abelian extensions of a given algebraic number field in a way that would generalize the so-called theorem of Kronecker and Weber (all abelian extensions of can be generated by roots of unity) and the extensions of imaginary quadratic fields (which may be generated from values of modular and elliptic functions related to elliptic curves with complex multiplication). The first part of the lecture is devoted to the fake conjecture that Hilbert made for imaginary quadratic fields. This is discussed both from a historical point of view (in that Hilbert’s authority prevented this error from being corrected for 14 years) and in mathematical terms, analyzing the algebro-geometric interpretations of the different statements and their respective traditions. After this, higher-dimensional analogues are discussed. Recent developments in this field (motives, etc., also Heegner points) are mentioned at the end.

MSC:
01A60Mathematics in the 20th century
11-03Historical (number theory)
11G15Complex multiplication and moduli of abelian varieties
11R37Class field theory for global fields