Details

Autor(en) / Beteiligte

• ESNAULT, HÉLÈNE
• KINDLER, LARS

Titel

Lefschetz theorems for tamely ramified coverings

Ist Teil von

• Proceedings of the American Mathematical Society, 2016-12, Vol.144 (12), p.5071-5080

Ort / Verlag

American Mathematical Society

Erscheinungsjahr

2016

Link zum Volltext

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• As is well known, the Lefschetz theorems for the étale fundamental group of quasi-projective varieties do not hold. We fill a small gap in the literature showing they do for the tame fundamental group. Let X be a regular projective variety over a field k, and let D\hookrightarrow X be a strict normal crossings divisor. Then, if Y is an ample regular hyperplane intersecting D transversally, the restriction functor from tame étale coverings of X\setminus D to those of Y\setminus D\cap Y is an equivalence if dimension X \ge 3, and is fully faithful if dimension X=2. The method is dictated by work of Grothendieck and Murre (1971). They showed that one can lift tame coverings from Y\setminus D\cap Y to the complement of D\cap Y in the formal completion of X along Y. One has then to further lift to X\setminus D.