Revista Matemática Complutense

, Volume 30, Issue 2, pp 217–232 | Cite as

Survey on some aspects of Lefschetz theorems in algebraic geometry

  • Hélène EsnaultEmail author


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


Fundamental group Lefschetz theorems Lisse sheaves Isocrystals 

Mathematics Subject Classification

14F20 14F45 14G17 14G99 



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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Copyright information

© Universidad Complutense de Madrid 2017

Authors and Affiliations

  1. 1.Freie Universität BerlinBerlinGermany

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