Georges Gras

activity

20212024

Φ

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

1 citations · 1 across the 4 of their papers we have counts for

collaborators

4 papers

math.NT2024

Initial layer of the anti-cyclotomic $Z_{3}$ -extension of $Q (- m)$ and capitulation phenomenon

Georges Gras

Let $k = Q (- m)$ be an imaginary quadratic field. We consider the properties of capitulation of the $p$ -class group of $k$ in the anti-cyclotomic $Z_{p}$ -extens…

math.NT2024

On the $Z_{p}$ -extensions of a totally $p$ -adic imaginary quadratic field -- With an appendix by Jean-François Jaulent

Georges Gras

Let $k = Q (- m)$ and $p \geq 3$ split in $k$ . We prove new properties of the $Z_{p}$ -extensions $K / k$ , distinct from the cyclotomic one; we do not assume $K/…

math.NT2023

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

Georges Gras

We consider, for real abelian fields K, the Birch--Tate formula linking the tame kernel \#K\_2(Z\_K) to $ζ$ \_K(-1); we compare, for quadratic and cyclic cubic fields with p=2,3, \#…

math.NT2021★ 1 cited

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

Georges Gras

We revisit, in an elementary way, the classical statement of various ``Main Conjectures'' for $p$ -class groups $H_{K}$ and $p$ -ramified torsion groups $T_{K}$ of ab…

Initial layer of the anti-cyclotomic Z3​-extension of Q(−m​) and capitulation phenomenon

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

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

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

Initial layer of the anti-cyclotomic $Z_{3}$ -extension of $Q (- m)$ and capitulation phenomenon

On the $Z_{p}$ -extensions of a totally $p$ -adic imaginary quadratic field -- With an appendix by Jean-François Jaulent

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