Bounds for the $\ell-torsion$ in class groups of number fields
星期四, 8 六月, 2017 - 10:30
Résumé :
Let $\ell$ and $d$ be a positive integers. By the Cohen Lenstra heuristics
the $\ell$-torsion part of the class groups of degree $d$ number fields should
be "very small" in terms of the discriminant for "almost all" such fields.
However, non-trivial such bounds for all $\ell$ are known only for
$d\leq 5$ due to recent work of Ellenberg, Pierce, and Wood. We explain
their strategy, and how one can improve their bounds
for $d=4, 5$. If time permits we also present analogous results for certain
families of arbitrarily large degree. (This is joint work with Christopher Frei).
Institution de l'orateur :
Royal Holloway Univ. of London
Thème de recherche :
Théorie des nombres
Salle :
Salle 4