<p>Let <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40993_2025_635_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="34" /> </InlineMediaObject> <EquationSource Format="TEX">$E/\mathbb {Q}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>E</mi> <mo stretchy="false">/</mo> <mi mathvariant="double-struck">Q</mi> </mrow> </math></EquationSource> </InlineEquation> be an elliptic curve and let <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40993_2025_635_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="42" /> </InlineMediaObject> <EquationSource Format="TEX">$p\ge 5$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>p</mi> <mo>≥</mo> <mn>5</mn> </mrow> </math></EquationSource> </InlineEquation> be a prime of good supersingular reduction. We generalize results due to Meng Fai Lim proving Kida’s formula and integrality results for characteristic elements of signed Selmer groups along the cyclotomic <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40993_2025_635_Article_IEq3.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">$\mathbb {Z}_p$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="double-struck">Z</mi> <mi>p</mi> </msub> </math></EquationSource> </InlineEquation>-extension of weakly ramified base fields <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40993_2025_635_Article_IEq4.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="43" /> </InlineMediaObject> <EquationSource Format="TEX">$K/\mathbb {Q}_p$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>K</mi> <mo stretchy="false">/</mo> <msub> <mi mathvariant="double-struck">Q</mi> <mi>p</mi> </msub> </mrow> </math></EquationSource> </InlineEquation>.</p>

On the cohomology of plus/minus Selmer groups of supersingular elliptic curves in weakly ramified base fields

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2025年5月20日

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Ben Forrás,
Katharina Müller

摘要

Let $E/\mathbb {Q}$ $E / Q$ be an elliptic curve and let $p\ge 5$ $p \geq 5$ be a prime of good supersingular reduction. We generalize results due to Meng Fai Lim proving Kida’s formula and integrality results for characteristic elements of signed Selmer groups along the cyclotomic $\mathbb {Z}_p$ $Z_{p}$ -extension of weakly ramified base fields $K/\mathbb {Q}_p$ $K / Q_{p}$ .