Survey on some aspects of Lefschetz theorems in algebraic geometry


We survey classical material around Lefschetz theorems for fundamental groups, and show the relation to parts of Deligne’s program in Weil II.

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It is a pleasure to thank Jakob Stix for a discussion on separable base points reflected in Sect. 3. We thank Tomoyuki Abe and Atsushi Shiho for discussions. We thank the public of the Santaló lectures at the Universidad Complutense de Madrid (October 2015) and the Rademacher lectures at the University of Pennsylvania (February 2016), where some points discussed in those notes were presented. In particular, we thank Ching-Li Chai for an enlightening discussion on compatible systems. We thank Moritz Kerz for discussions we had when we tried to understand Deligne’s program in Weil II while writing [11]. We thank the two referees for their friendly and thorough reports which helped us to improve the initial version of these notes.

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Correspondence to Hélène Esnault.

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Esnault, H. Survey on some aspects of Lefschetz theorems in algebraic geometry. Rev Mat Complut 30, 217–232 (2017).

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  • Fundamental group
  • Lefschetz theorems
  • Lisse sheaves
  • Isocrystals

Mathematics Subject Classification

  • 14F20
  • 14F45
  • 14G17
  • 14G99