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SUMMARY:Emiliano Ambrosi (Strasbourg)
DTSTART:20231213T160000Z
DTEND:20231213T170000Z
DTSTAMP:20260418T064529Z
UID:LNTS/112
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/LNTS/112/">R
 eduction modulo p of the Noether problem</a>\nby Emiliano Ambrosi (Strasbo
 urg) as part of London number theory seminar\n\nLecture held in Room 140\,
  the Huxley Building\, Imperial College London.\n\nAbstract\nLet k be an a
 lgebraically closed field of characteristic p≥0 and V a faithful k-ratio
 nal representation of an l-group G. The Noether's problem asks whether V/G
  is (stably) birational to a point. If l is equal to p\, then Kuniyoshi pr
 oved that this is true\, while\, if l is different from p\, Saltman constr
 ucted l-groups for which V/G is not stably rational. Hence\, the geometry 
 of  V/G depends heavily on  the characteristic of the field. We show that 
 for all the groups G constructed by Saltman\, one cannot interpolate betwe
 en the Noether problem in characteristic 0 and p. More precisely\, we show
  that it does not exist a complete valuation ring R of mixed characteristi
 c (0\,p) and a smooth proper R-scheme X---->Spec(R) whose special fiber an
 d generic fiber are both stably birational to V/G. The proof combines the 
 integral p-adic Hodge theoretic results of Bhatt-Morrow-Scholze\, with the
  study of the Cartier operator on differential forms in positive character
 istic. This is a joint work  with Domenico Valloni.\n
LOCATION:https://researchseminars.org/talk/LNTS/112/
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