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Register a new userComputations of Orbits for the Lubin-Tate Ring
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We take a direct approach to computing the orbits for the action of the automorphism group $mathbb{G}_2$ of the Honda formal group law of height $2$ on the associated Lubin-Tate rings $R_2$. We prove that $(R_2/p)_{mathbb{G}_2} cong mathbb{F}_p$. The result is new for $p=2$ and $p=3$. For primes $pgeq 5$, the result is a consequence of computations of Shimomura and Yabe and has been reproduced by Kohlhaase using different methods.
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We show that Lubin-Tate spectra at the prime $2$ are Real oriented and Real Landweber exact. The proof is by application of the Goerss-Hopkins-Miller theorem to algebras with involution. For each height $n$, we compute the entire homotopy fixed point spectral sequence for $E_n$ with its $C_2$-action given by the formal inverse. We study, as the height varies, the Hurewicz images of the stable homotopy groups of spheres in the homotopy of these $C_2$-fixed points.
We study certain formal group laws equipped with an action of the cyclic group of order a power of $2$. We construct $C_{2^n}$-equivariant Real oriented models of Lubin-Tate spectra $E_h$ at heights $h=2^{n-1}m$ and give explicit formulas of the $C_{2^n}$-action on their coefficient rings. Our construction utilizes equivariant formal group laws associated with the norms of the Real bordism theory $MU_{mathbb{R}}$, and our work examines the height of the formal group laws of the Hill-Hopkins-Ravenel norms of $MU_{mathbb{R}}$.
We completely compute the slice spectral sequence of the $C_4$-spectrum $BP^{((C_4))}langle 2 rangle$. After periodization and $K(4)$-localization, this spectrum is equivalent to a height-4 Lubin-Tate theory $E_4$ with $C_4$-action induced from the Goerss-Hopkins-Miller theorem. In particular, our computation shows that $E_4^{hC_{12}}$ is 384-periodic.
We study the reduction modulo $l$ of some elliptic representations; for each of these representations, we give a particular lattice naturally obtained by parabolic induction in giving the graph of extensions between its irreducible sub-quotient of its reduction modulo $l$. The principal motivation for this work, is that these lattices appear in the cohomology of Lubin-Tate towers.
Let $F$ be a finite extension of $mathbb{Q}_p$. We determine the Lubin-Tate $(varphi,Gamma)$-modules associated to the absolutely irreducible mod $p$ representations of the absolute Galois group ${rm Gal}(bar{F}/F)$.
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