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Yoshiyasu Ozeki
Bounds on torsion of CM abelian varieties over a p-adic field with values
in a field of p-power roots
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print
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| Published: |
March 8, 2024. |
| Keywords: |
abelian varieties, complex multiplication, p-adic Hodge theory. |
| Subject [2010]: |
11G10, 14K22. |
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Abstract
Let p be a prime number and M the extension field of a p-adic field K obtained
by adjoining all p-power roots of all elements of K. In this paper, we show that
there exists a constant C, depending only on K and an integer g>0, which satisfies
the following property: If A/K is a g-dimensional CM abelian variety,
then the order of the torsion subgroup of A(M) is bounded by C.
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| Acknowledgements
This work is supported by JSPS KAKENHI Grant Number JP19K03433.
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| Author information
Yoshiyasu Ozeki
Faculty of Science
Kanagawa University
3-27-1 Rokkakubashi, Kanagawa-ku
Yokohama-shi, Kanagawa 221-8686, JAPAN
ozeki@kanagawa-u.ac.jp
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