Georges Gras

Documents

Publications

	On the Zp-extensions of a totally p-adic imaginary quadratic field -- With an appendix by Jean-François Jaulent Georges Gras 2024 Pré-publication, Document de travail hal-04518815v2
	On the Real Abelian Main Conjecture in the non semi-simple case Georges Gras 2023 Pré-publication, Document de travail hal-04133044v1
	Exceptional case of the non semi-simple Real Abelian Main Conjecture Georges Gras 2023 Pré-publication, Document de travail hal-04178551v1
	Genus theory of p-adic pseudo-measures -- Tame kernels and abelian p-ramification Georges Gras 2023 Pré-publication, Document de travail hal-04237257v2
	Unlimited lists of fundamental units of quadratic fields - Applications to some arithmetic properties Georges Gras 2023 Pré-publication, Document de travail hal-03705446v2
	Algebraic norm and capitulation of p-class groups in ramified cyclic p-extensions Georges Gras 2023 Pré-publication, Document de travail hal-03865383v3
	New characterization of the norm of the fundamental unit of Q(M^1/2). Georges Gras 2023 Pré-publication, Document de travail hal-04108717v1
	The Chevalley--Herbrand formula and the real abelian Main Conjecture Georges Gras 2022 Pré-publication, Document de travail hal-03739451v3
	Application of the notion of ϕ-object to the study of p-class groups and p-ramified torsion groups of abelian extensions Georges Gras 2022 Pré-publication, Document de travail hal-03466431v5
	Tate–Shafarevich groups in the cyclotomic Z^-extension and Weber’s class number problem Georges Gras 2021 Pré-publication, Document de travail hal-02935539v3
	On the λ-stability of p-class groups along cyclic p-towers of a number field Georges Gras 2021 Pré-publication, Document de travail hal-03155190v5
	Algorithmic complexity of Greenberg's conjecture Georges Gras 2020 Pré-publication, Document de travail hal-02541269v4
	The p-rank ε-conjecture on class groups is true for towers of p-extensions Georges Gras 2020 Pré-publication, Document de travail hal-02444876v2
	Practice of incomplete p-ramification over a number field -- History of abelian p-ramification Georges Gras 2019 Pré-publication, Document de travail hal-02106964v3
	Successive maxima of the non-genus part of class numbers Georges Gras 2019 Pré-publication, Document de travail hal-02384974v1
	Note on some p-invariants of Q(N^{1/p}) using reflection theorem Georges Gras 2019 Pré-publication, Document de travail hal-02301429v1
	Genus theory and ε-conjectures on p-class groups Georges Gras 2019 Pré-publication, Document de travail hal-02059441v3
	Heuristics and conjectures in direction of a p-adic Brauer--Siegel theorem Georges Gras 2018 Pré-publication, Document de travail hal-01682891v3
	Test of Vandiver's conjecture with Gauss sums -- Heuristics Georges Gras 2018 Pré-publication, Document de travail hal-01856083v4
	On the order modulo p of an algebraic number Georges Gras 2017 Pré-publication, Document de travail hal-01225061v2
	Approche p-adique de la conjecture de Greenberg pour les corps totalement réels Georges Gras 2017 Pré-publication, Document de travail hal-01404933v3
	On p-rationality of number fields. Applications-PARI/GP programs Georges Gras 2017 Pré-publication, Document de travail hal-01590183v2
	The p-adic Kummer-Leopoldt constant -- Normalized p-adic regulator Georges Gras 2017 Pré-publication, Document de travail hal-01444560v2
	SUR LE MODULE DE BERTRANDIAS–PAYAN DANS UNE p-EXTENSION – NOYAU DE CAPITULATION Georges Gras 2016 Pré-publication, Document de travail hal-01261993v1
	NO RIEMANN-HURWITZ FORMULA FOR THE p-RANKS OF RELATIVE CLASS GROUPS Georges Gras 2015 Pré-publication, Document de travail hal-01243887v1
	SUR LE MODULE DE BERTRANDIAS–PAYAN DANS UNE p-EXTENSION – NOYAU DE CAPITULATION Georges Gras 2015 Pré-publication, Document de travail hal-01216984v1
	Les $\theta$-régulateurs locaux d'un nombre algébrique. Conjectures p-adiques Georges Gras 2014 Pré-publication, Document de travail hal-00936889v3
	Etude probabiliste des p-quotients de Fermat Georges Gras 2014 Pré-publication, Document de travail hal-01062305v2
	On the structure of the Galois group of the Abelian closure of a number field Georges Gras 2013 Pré-publication, Document de travail hal-00764649v4

	Normes d'idéaux dans la tour cyclotomique et conjecture de Greenberg Georges Gras Annales mathématiques du Québec, 2019, Ann. math. du Québec, 43, pp.249-280. ⟨10.1007/s40316-018-0108-3⟩ Article dans une revue hal-01546656v3
	Annihilation of tor_p(G_S^ab) for real abelian extensions K/Q Georges Gras Communications in Advanced Mathematical Sciences, 2018, Communications in Advanced Mathematical Sciences, 1 (1), pp.5 - 34. ⟨10.33434/cams.441035⟩ Article dans une revue hal-01807711v2
	Invariant generalized ideal classes – structure theorems for p-class groups in p-extensions Georges Gras Proceedings Mathematical Sciences, 2017, Proceedings - Mathematical Sciences, 127 (1), pp.1-34. ⟨10.1007/s12044-016-0324-1⟩ Article dans une revue hal-03317756v1
	Local theta-regulators of an algebraic number -- p-adic Conjectures Georges Gras Canadian Journal of Mathematics., 2016, Vol. 68 (3), pp.571-624 Article dans une revue hal-01429498v1
	Some works of Furtwängler and Vandiver revisited and Fermat's last theorem Georges Gras , Roland Quême Publications Mathématiques UFR Sciences Techniques Besançon, 2012, 2, pp.47-110 Article dans une revue hal-00578783v2
	Stickelberger's congruences for absolute norms of relative discriminants Georges Gras Journal de Théorie des Nombres de Bordeaux, 2010, 22 (2), pp.397-402. ⟨10.5802/jtnb.723⟩ Article dans une revue hal-00578984v1
	Analysis of the classical cyclotomic approach to fermat's last theorem Georges Gras Publications Mathématiques UFR Sciences Techniques Besançon, 2010, 2010, pp.85-119 Article dans une revue hal-00578969v1
	Principalization of ideals in abelian extensions of number fields Sebastien Bosca , Georges Gras , Jean-François Jaulent International Journal of Number Theory, 2009, 5, pp.1--13 Article dans une revue hal-00267830v2
	Note on 2-rational fields Georges Gras , Jean-François Jaulent Journal of Number Theory, 2009, 129 (2), pp.495-498 Article dans une revue hal-00278094v1
	Ramifications minimales Georges Gras J. Théor. Nombres Bordx, 2000, 12 (2), pp.423--435 Article dans une revue hal-00260867v1
	Théorèmes de réflexion. Georges Gras J. Théor. Nombres Bordx, 1998, 10 (2), pp.399--499 Article dans une revue hal-00260892v1
	Interprétation et calcul du groupe de défaut d'un principe de Hasse Anne Cortella , Georges Gras Mathematical News / Mathematische Nachrichten, 1997, 188, pp.109-140. ⟨10.1002/mana.19971880108⟩ Article dans une revue hal-00795836v1

	Class field theory: From theory to practice Georges Gras Springer, pp.507, 2005 Ouvrages hal-00259968v1

	Sur les l-classes d'idéaux dans les extensions cycliques relatives de degré premier l Georges Gras Modélisation et simulation. Université Joseph-Fourier - Grenoble I, 1972 HDR tel-00284188v1

Georges Gras

Publications

On the Zp-extensions of a totally p-adic imaginary quadratic field -- With an appendix by Jean-François Jaulent

On the Real Abelian Main Conjecture in the non semi-simple case

Exceptional case of the non semi-simple Real Abelian Main Conjecture

Genus theory of p-adic pseudo-measures -- Tame kernels and abelian p-ramification

Unlimited lists of fundamental units of quadratic fields - Applications to some arithmetic properties

Algebraic norm and capitulation of p-class groups in ramified cyclic p-extensions

New characterization of the norm of the fundamental unit of Q(M^1/2).

The Chevalley--Herbrand formula and the real abelian Main Conjecture

Application of the notion of ϕ-object to the study of p-class groups and p-ramified torsion groups of abelian extensions

Tate–Shafarevich groups in the cyclotomic Z^-extension and Weber’s class number problem

On the λ-stability of p-class groups along cyclic p-towers of a number field

Algorithmic complexity of Greenberg's conjecture

The p-rank ε-conjecture on class groups is true for towers of p-extensions

Practice of incomplete p-ramification over a number field -- History of abelian p-ramification

Successive maxima of the non-genus part of class numbers

Note on some p-invariants of Q(N^{1/p}) using reflection theorem

Genus theory and ε-conjectures on p-class groups

Heuristics and conjectures in direction of a p-adic Brauer--Siegel theorem

Test of Vandiver's conjecture with Gauss sums -- Heuristics

On the order modulo p of an algebraic number

Approche p-adique de la conjecture de Greenberg pour les corps totalement réels

On p-rationality of number fi elds. Applications-PARI/GP programs

The p-adic Kummer-Leopoldt constant -- Normalized p-adic regulator

SUR LE MODULE DE BERTRANDIAS–PAYAN DANS UNE p-EXTENSION – NOYAU DE CAPITULATION

NO RIEMANN-HURWITZ FORMULA FOR THE p-RANKS OF RELATIVE CLASS GROUPS

SUR LE MODULE DE BERTRANDIAS–PAYAN DANS UNE p-EXTENSION – NOYAU DE CAPITULATION

Les $\theta$-régulateurs locaux d'un nombre algébrique. Conjectures p-adiques

Etude probabiliste des p-quotients de Fermat

On the structure of the Galois group of the Abelian closure of a number field

Normes d'idéaux dans la tour cyclotomique et conjecture de Greenberg

Annihilation of tor_p(G_S^ab) for real abelian extensions K/Q

Invariant generalized ideal classes – structure theorems for p-class groups in p-extensions

Local theta-regulators of an algebraic number -- p-adic Conjectures

Some works of Furtwängler and Vandiver revisited and Fermat's last theorem

Stickelberger's congruences for absolute norms of relative discriminants

Analysis of the classical cyclotomic approach to fermat's last theorem

Principalization of ideals in abelian extensions of number fields

Note on 2-rational fields

Ramifications minimales

Théorèmes de réflexion.

Interprétation et calcul du groupe de défaut d'un principe de Hasse

Class field theory: From theory to practice

Sur les l-classes d'idéaux dans les extensions cycliques relatives de degré premier l

On p-rationality of number fields. Applications-PARI/GP programs