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SUMMARY:Birational Maps of Severi-Brauer Surfaces\, with Applications to C
 remona Groups of Higher Rank - Julia Schneider\, Universität Zürich
DTSTART:20240228T141500Z
DTEND:20240228T151500Z
UID:TALK207028@talks.cam.ac.uk
CONTACT:Holly Krieger
DESCRIPTION:We describe the group of birational transformations of a non-t
 rivial Severi-Brauer surface over a perfect field\, proving that if it con
 tains a point of degree 6\, then it is not generated by elements of finite
  order. We then use this result to study Mori fibre spaces over the field 
 of complex numbers and deduce that the Cremona group of rank at least 4 ad
 mits any group (of cardinality at most $|\\mathbb{C}|$) as a quotient. Mor
 eover\, we prove that the 3-torsion in the abelianization of the  Cremona 
 group of rank at least 4 is uncountable. This is based on a joint work wit
 h J. Blanc and E. Yasinsky.
LOCATION:CMS MR13
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