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SUMMARY:On finite presentation for the tame fundamental group - Vasudevan 
 Srinivas (Tata Institute of Fundamental Research)
DTSTART:20220617T103000Z
DTEND:20220617T113000Z
UID:TALK174944@talks.cam.ac.uk
DESCRIPTION:This is a report on joint work with H. Esnault and M. Schuster
 man.\nRecall that the etale fundamental group of a variety over an algebra
 ically closed field of characteristic 0 is known to be a finitely presente
 d profinite group\; this is proved by first reducing to varieties over the
  complex numbers\, and then comparing with the topological fundamental gro
 up. In positive characteristics\, even if we restrict to smooth varieties\
 , finite generation fails in general for etale fundamental groups of non-p
 roper varieties (eg\, for the affine line).\nFor a smooth variety with a s
 mooth\, projective compactification with a SNC boundary divisor\, we show 
 that the tame fundamental group is a finitely presented profinite group. I
 n particular\, this holds for the fundamental groups of smooth projective 
 varieties.
LOCATION:Seminar Room 1\, Newton Institute
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