Pointwise bound for ℓ-torsion in class groups: Elementary abelian extensions
2020 ◽
Vol 0
(0)
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AbstractElementary abelian groups are finite groups in the form of {A=(\mathbb{Z}/p\mathbb{Z})^{r}} for a prime number p. For every integer {\ell>1} and {r>1}, we prove a non-trivial upper bound on the {\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, the {\ell}-torsion in class groups are bounded non-trivially for every G-extension and every integer {\ell>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.
2010 ◽
Vol 20
(05)
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pp. 671-688
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2015 ◽
Vol 11
(04)
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pp. 1177-1215
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2018 ◽
Vol 28
(08)
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pp. 1693-1703
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2011 ◽
Vol 10
(03)
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pp. 377-389
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2018 ◽
Vol 17
(10)
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pp. 1850184
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2018 ◽
Vol 167
(02)
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pp. 229-247
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2008 ◽
Vol 07
(06)
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pp. 735-748
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2018 ◽
Vol 17
(08)
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pp. 1850146
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