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SUMMARY:Alexander Petrov (Harvard)
DTSTART:20210304T160000Z
DTEND:20210304T172000Z
DTSTAMP:20260423T021309Z
UID:RAMpAGe/33
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/RAMpAGe/33/"
 >Geometrically irreducible $p$-adic local systems are de Rham up to a twis
 t</a>\nby Alexander Petrov (Harvard) as part of Recent Advances in Modern 
 p-Adic Geometry (RAMpAGe)\n\n\nAbstract\nLet $K$ be a p-adic field. Althou
 gh there are plenty of non-de Rham representations of the Galois group of 
 $K$\, it turns out that for any smooth variety $X$ over $K$ and a $\\overl
 ine{\\mathbf{Q}}_p$-local system $L$ on $X$ such that the restriction of $
 L$ to $X_{\\overline{K}}$ is irreducible\, there exists a character of the
  Galois group of $K$ such that twisting by this character turns $L$ into a
  de Rham local system. In particular\, for a geometrically irreducible $\\
 overline{\\mathbf{Q}}_p$-local system on a smooth variety over a number fi
 eld\, the associated projective representation of the fundamental group au
 tomatically satisfies the assumptions of the relative Fontaine-Mazur conje
 cture.\n\nThe proof uses $p$-adic Riemann-Hilbert correspondence in the fo
 rm constructed by Liu and Zhu as well as its logarithmic version construct
 ed by Diao-Lan-Liu-Zhu and their decompletions developed by Shimizu.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/33/
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