English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Elementary abelian groups are finite groups in the form ofA=(ℤ/p⁢ℤ)r{A=(\mathbb{Z}/p\mathbb{Z})^{r}}for a prime number  p . For every integerℓ&gt;1{\ell&gt;1}andr&gt;1{r&gt;1}, we prove a non-trivial upper bound on theℓ{\ell}-torsion in class groups of every  A -extension. Our results are pointwise and unconditional. This establishes the first case where for some Galois group  G , theℓ{\ell}-torsion in class groups are bounded non-trivially for every  G -extension and every integerℓ&gt;1{\ell&gt;1}. When  r  is large enough, the unconditional pointwise bound we obtain also breaks the previously best known bound shown by Ellenberg and Venkatesh under GRH.

Pointwise bound for ℓ-torsion in class groups: Elementary abelian extensions