Section:
New Results
Logarithmic Class Groups
Logarithmic class groups and units, introduced by Jaulent in 1994, are an
intriguing -adic variation on the classical class and unit groups
related to Iwasawa theory and the wild kernels of algebraic -theory.
These -modules of finite type provide direct access to invariants
studied in standard conjectures about -extensions.
In [12] we devised a new algorithm to explicitly
compute them in subexponential time under standard conjectures (GRH and
Gross-Kuz'min) and to validate unconditionaly the computed results
(now in exponential time). The algorithm has been implementated in the
PARI/GP system.