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SUMMARY:Daishi Kiyohara (Harvard University)
DTSTART:20260921T200000Z
DTEND:20260921T210000Z
DTSTAMP:20261004T234733Z
UID:NTBU/53
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NTBU/53/">Fo
 rmal groups and $(\\varphi\,\\Gamma)$-modules</a>\nby Daishi Kiyohara (Har
 vard University) as part of Boston University Number Theory Seminar\n\nLec
 ture held in CDS Room 365 in Boston University.\n\nAbstract\nUsing the cyc
 lotomic tower\, Fontaine introduced $(\\varphi\,\\Gamma)$-modules\, which 
 constitute a category equivalent to the category of Galois representations
  of a $p$-adic local field $K$.\nIn this talk\, I will explain a generaliz
 ation to torsion towers of a one-dimensional formal group $H$.\nI will fir
 st define the exponential period map of $H$ and use it to construct a comp
 lete local ring $R_H$ with commuting actions of $\\varphi$ and $\\Gamma=\\
 mathrm{Gal}(K(H[p^\\infty](\\overline{K}))/K)$.\nThe main theorem is an eq
 uivalence of categories between \\'{e}tale $(\\varphi\,\\Gamma)$-modules o
 ver $R_H$ and finitely generated $\\mathcal{O}_K$-modules with a continuou
 s $\\mathrm{Gal}_K$-action\, which recovers the classical equivalence in t
 he multiplicative case $H=\\widehat{\\mathbb{G}}_m$.\nI will highlight new
  phenomena which arise in cases of higher height\, such as higher Krull di
 mensions of $R_H$.\n
LOCATION:https://researchseminars.org/talk/NTBU/53/
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