Algebraic Number Theory
Created on February 1st, 2013.
I am going to put here some old papers and/or write down errata and/or
comments.
Numbers inside brackets ([Nb]) refer to my
publication list.
BOURBAKI SEMINAR.
- [ 5]
Un contre-exemple à une conjecture d'E. Noether.
Séminaire Bourbaki 1969-1970, exp. 372, 145-154,
Numdam.
- [ 9]
Bases normales et constante de l'équation fonctionnelle
des fonctions L d'Artin.
Séminaire Bourbaki 1973-1974, exp. 450, 273-294.
Numdam.
GALOIS MODULES.
-
[ 3]
Sur l'arithmétique des extensions galoisiennes à
groupe de Galois diédral d'ordre 2p.
Ann. Inst. Fourier 19,1 (1969), 1--80.
Numdam.
-
[ 4]
Anneau des entiers d'une extension galoisienne considéré
comme module sur l'algèbre du groupe de Galois.
Mémoire de la SMF 25 (1971), 123--126.
Numdam.
-
[ 7]
Modules sur l'algèbre du groupe quaternionien.
Ann. Sc. E.N.S. 4 (1971), 399-408.
Numdam,
postscript .
- [ 8]
Sur les extensions à groupe de Galois quaternionien.
C.R. Acad. Sc. Paris 274 (1972), 933-935.
postscript ,
pdf .
-
Corrigendum for [7] and [8],
dvi ,
postscript ,
pdf ,
then (most of)
the proofs for [8],
first on line Jan. 16th, 2015,
dvi ,
postscript ,
pdf .
-
[10]
Character Theory and Artin $L$-functions.
In Algebraic Number Fields (Fröhlich ed.),
Academic Press, New-York (1977), 1-80. pdf;
if pdf-file looks unavailable, try ps-file here:
postscript , but loading ps needs about 7 minutes.
- [11]
H8, same book, 525-538.
postscript ,
pdf .
DISCRIMINANTS.
-
[14]
Petits discriminants.
Ann. Inst. Fourier 29,1 (1979), 159--170.
Numdam.
-
[16, not online]
Lenstra's constant and Euclidean number fields
(with Armin Leutbecher) .
Astérisque 29,1 (1982), 87--131.
ERRATUM:
dvi ,
postscript ,
pdf .
-
[19]
Méthodes géométriques dans la recherche des petits discriminants .
Séminaire de Théeorie des Nombres de Paris 1983--84,
Birkhäuser, Basel (1985), 147--179.
pdf.
-
[20]
Formes quadratiques et extensions en caractéristique 2
(with Anne-Marie BERGÉ)
.
Ann. Inst. Fourier 35,2 (1985), 57--77.
Numdam.
ERRATUM:
dvi ,
postscript ,
pdf .
- [21]
Sur les corps résolubles de degré premier
(with Soun-Hi Kwon).
J. reine angew. Math. 375/376 (1985), 12--23;
postscript ,
pdf .
REMARK:
dvi ,
ps ,
pdf .
- [29]
Les discriminants quadratiques
et la congruence de Stickelberger.
J. Th Nombres Bordeaux 1 (1979), 197--204,
Numdam;
COMPLEMENT: dvi,
postscript,
pdf.
HEURISTICS.
Here are the four joint papers [22], [23], [28], [34]
(with Henri Cohen)
devoted to heuristics on class groups,
among which [23] is just a survey delivered by the second author
at a congress held in Stift Rein (near Graz, Austria),
21--26 September, 1986.
- [22]
Class Groups of Number Fields: Numerical Heuristics.
Math. Comp. 48 (1987), 123--137.
pdf ,
postscript .
- [23]
Ein heuristisches Studium der Klassengruppen.
Forschungsgesellschaft Joanneum Berichte, Graz (1987), 60--69.
pdf ,
postscript .
- [28]
Étude heuristique des groupes de classes.
J. reine angew. Math. 404 (1990), 39--76.
pdf ,
postscript
(needs about 1mn50s loading).
- [34]
Heuristics on Class Groups: Some Good Primes are not too Good.
Math. Comp 63 (1994), 329--334.
pdf ,
postscript .
VARIA.
- [26]
Notions relatives de régulateurs et de hauteurs
(with A.-M. Bergé).
Acta Arith. 54 (1989), 155--170.
pdf.
Complements to this paper may be found in the following
two joint seminar talks with
A.-M. Bergé :
[25, not online]
Sur les minorations géométriques des régulateurs
,
Sém. Th. Nombres Paris 1987/1988, Birkhäuser, Basel (1989), 23--50,
and
[27]
Minorations de hauteurs et petits régulateurs relatifs,
Sém. Th. Nombres Bordeaux (1987/1988), 28 pp.
Gött. Digital.
In these papers we introduced the notion of a relative regulator
and were lead to the Conjecture: relative regulators
are bounded from below independently of the base field.
An important partial result has been proved
by Eduardo Friedman and Nils Skloruppa; see
Relative regulators of number fields,
Invent. Math 135 (1999), 115--144.
[Due to their analytic point of view, these authors make use
of a notion of relative regulator which slightly differs from ours,
inspired by geometry on numbers,
but the problems of the existence of a lower bound are basically the same.]
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