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SUMMARY:Mathieu Florence (Jussieu)
DTSTART:20210629T150000Z
DTEND:20210629T155000Z
DTSTAMP:20260413T062825Z
UID:zoomnovy/5
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/zoomnovy/5/"
 >Heisenberg representations and indecomposable division algebras</a>\nby M
 athieu Florence (Jussieu) as part of Algebraic groups and algebraic geomet
 ry: in honor of Zinovy Reichstein's 60th birthday\n\n\nAbstract\nLet $F$ b
 e a field\, with absolute Galois group G. Let $p$ be a prime. Denote by $B
 _d$ the Borel subgroup of $GL_d$\, and by $U_d$ its unipotent radical. We 
  consider the question of lifting a triangular Galois representation $G \\
 longrightarrow B_d(\\mathbb Z/p)$\, to its mod $p^2$ analogue $G \\longrig
 htarrow B_d(\\mathbb Z/p^2)$. It has a rich history\, which we will recall
 . We'll then explain positive results\, up to  $d=3$\, under the presence 
 of $p^2$-th root of unity in $F$. Using an indecomposability result for di
 visions algebras\, due to Karpenko\, we'll show that the answer to the ana
 logous question\, with $U_3$ in place of $B_3$\, is negative.\n
LOCATION:https://researchseminars.org/talk/zoomnovy/5/
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