Finite presentation of the tame fundamental group

• Hélène Esnault ^[2] ; Mark Shusterman ^[1] ; Vasudevan Srinivas ^[3]
  1. [1] Harvard University

     Harvard University

     City of Cambridge, Estados Unidos

     
  2. [2] Freie Universität Berlin, Alemania
  3. [3] School of Mathematics, TIFR, India

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• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 28, Nº. 2, 2022
• Idioma: inglés
• DOI: 10.1007/s00029-021-00732-4
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• Resumen

  • Let p be a prime number, and let k be an algebraically closed field of characteristic p. We show that the tame fundamental group of a smooth affine curve over k is a projective profinite group. We prove that the fundamental group of a smooth projective variety over k is finitely presented; more generally, the tame fundamental group of a smooth quasi-projective variety over k, which admits a good compactification, is finitely presented.