Lubin-Tate formal groups and $p$-adic Galois representations


Yi Ouyang

13:40:00 - 14:30:00

101 , Mathematics Research Center Building (ori. New Math. Bldg.)

In $p$-adic Hodge theory, the theory of cyclotomic $\mathbb{Z}_p$-extensions plays an essential role in the construction of fields of norms and $(\varphi,\Gamma)$- modules associated to $p$-adic Galois representations. In this talk we discuss the generalization to Lubin-Tate extensions and establish generalized theorems of Fontaine and others in this aspect, especially the theorem about the categorical equivalence of etale $(\varphi,\Gamma)$-modules and $p$-adic Galois representations. We also discuss Lubin- Tate elements in $p$-adic Hodge theory and show that $B_{e,h}$, a generalization of $B_e$, is principal.

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