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ON THE TEMPERED FUNDAMENTAL GROUPS OF HYPERBOLIC CURVES OF GENUS
$0$ OVER 
$\overline {\mathbb {Q}}_p$
- Part of
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- Journal:
- Journal of the Institute of Mathematics of Jussieu / Volume 22 / Issue 6 / November 2023
- Published online by Cambridge University Press:
- 01 June 2022, pp. 2833-2856
- Print publication:
- November 2023
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Let p be a prime number. In the present paper, we prove that the moduli of hyperbolic curves of genus
$0$ over an algebraic closure of the field of p-adic numbers may be completely determined by their tempered fundamental groups.
The
$\mathbb{Z}/p$ metabelian birational 
$p$-adic section conjecture for varieties
- Part of
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- Journal:
- Compositio Mathematica / Volume 153 / Issue 7 / July 2017
- Published online by Cambridge University Press:
- 04 May 2017, pp. 1433-1445
- Print publication:
- July 2017
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We generalize the
$\mathbb{Z}/p$metabelian birational 
$p$-adic section conjecture for curves, as introduced and proved in Pop [On the birational
$p$-adic section conjecture, Compos. Math. 146 (2010), 621–637], to all complete smooth varieties, provided 
$p>2$. The condition 
$p>2$ seems to be of technical nature only, and might be removable.
On the birational p-adic section conjecture
- Part of
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- Journal:
- Compositio Mathematica / Volume 146 / Issue 3 / May 2010
- Published online by Cambridge University Press:
- 18 March 2010, pp. 621-637
- Print publication:
- May 2010
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