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<p>Let <i>X</i> be a proper scheme of finite type over <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb {Q}_p\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="double-struck">Q</mi> <mi>p</mi> </msub> </math></EquationSource> </InlineEquation> and let <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(f : X \rightarrow X\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>f</mi> <mo>:</mo> <mi>X</mi> <mo stretchy="false">→</mo> <mi>X</mi> </mrow> </math></EquationSource> </InlineEquation> be a morphism. When <i>K</i> is a finite extension of <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mathbb {Q}_p\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="double-struck">Q</mi> <mi>p</mi> </msub> </math></EquationSource> </InlineEquation>, the boundedness of <i>f</i>-periods in <i>X</i>(<i>K</i>) is a well studied question. In this note, we study the boundedness of <i>f</i>-periods in <i>X</i>(<i>K</i>) when <i>K</i> is an (possibly infinite) algebraic extension of <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\mathbb {Q}_p\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="double-struck">Q</mi> <mi>p</mi> </msub> </math></EquationSource> </InlineEquation> with finite residue field.</p>

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On boundedness of periods of self maps of algebraic varieties

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年10月31日

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  • Manodeep Raha

摘要

Let X be a proper scheme of finite type over \(\mathbb {Q}_p\) Q p and let \(f : X \rightarrow X\) f : X → X be a morphism. When K is a finite extension of \(\mathbb {Q}_p\) Q p , the boundedness of f-periods in X(K) is a well studied question. In this note, we study the boundedness of f-periods in X(K) when K is an (possibly infinite) algebraic extension of \(\mathbb {Q}_p\) Q p with finite residue field.