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<p>Let <i>p</i> be a fixed odd prime and let <i>K</i> be an imaginary quadratic field in which <i>p</i> splits. Let <i>A</i> be an abelian variety defined over <i>K</i> with supersingular reduction at both primes above <i>p</i> in <i>K</i>. Under certain assumptions, we give a growth estimate for the Mordell–Weil rank of <i>A</i> over finite extensions inside the ℤ<Stack> <sub><i>p</i></sub> <sup>2</sup> </Stack>-extension of <i>K</i>. In the last section, written by Chris Williams, he includes some speculative remarks on the <i>p</i>-adic <i>L</i>-functions for GSp(4) corresponding to the multi-signed Selmer groups constructed in this paper.</p>

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On the Mordell–Weil ranks of supersingular abelian varieties over ℤ p 2 -extensions

  • 期刊论文

  • 发表日期：

    2025年6月29日

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  • Cédric Dion,
  • Jishnu Ray

摘要

Let p be a fixed odd prime and let K be an imaginary quadratic field in which p splits. Let A be an abelian variety defined over K with supersingular reduction at both primes above p in K. Under certain assumptions, we give a growth estimate for the Mordell–Weil rank of A over finite extensions inside the ℤ p 2 -extension of K. In the last section, written by Chris Williams, he includes some speculative remarks on the p-adic L-functions for GSp(4) corresponding to the multi-signed Selmer groups constructed in this paper.