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  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.