论文标题
在澳大利亚人的许多基本情况下，某些物体的构造
A construction of some objects in many base cases of an Ausoni-Rognes conjecture
论文作者
论文摘要
让$ p $为素数，$ n \ geq 1 $，$ k（n）$ n $ n $ th morava $ k $ - 理论频谱，$ \ mathbb {g} _n $扩展的摩拉瓦稳定器组和$ k（a）$ elgebraic $ k $ k $ - $ k $ - $ s $ s $ s $ s $ -a $ -a $ a $ a $ a。对于$ n+1 $ 1 $复杂$ v_n $，Ausoni和Rognes指出（a）单位映射$ i_n：l_ {k（n）}（s^0）（s^0）\ to e_n $从$ k（n）$ - 本地领域 - lubin-tate spectrum to lubin-tate Specter to lubin-tate Specte a Map to to to to t to ph [k（n） v_ {n+1}^{ - 1} v_n \ to（k（e_n））^{h \ mathbb {g} _n} \ wedge v_ {n+1}^{ - 1}^{ - 1} v_n \] v_n} v_n \]，这是一个弱等价$（k（e_n））^{h \ mathbb {g} _n} $表示连续的同型固定点光谱，并且（c）$π_\ ast（ - ast（ - ）$是上述映射的目标是同质固定点频谱序列的基台。对于$ n = 1 $，$ p \ geq 5 $和$ v_1 = v（1）$，我们通过证明$ i_1 $诱导映射\ [k（l_ {k（k（k（k（k（s^0））（s^0））\ wedge v_ v_ v_ v_ {2}^{2}^{2}^{-1} v_1（k（k）） v_ {2}^{ - 1} v_1）^{h \ mathbb {g} _1}，\]，其中该地图的目标是连续的同型固定点光谱，具有相关的同型固定点光谱序列。另外，我们证明存在一个等价\ [（k（e_1）\ wedge v_ {2}^{ - 1} v_1） v_2^{ - 1} v_1，\]其中$（k（e_1））^{\ widetilde {h} \ mathbb {g} _1} $是$ \ mathbb {g} _1 _1 _1 $的固定点。
Let $p$ be a prime, $n \geq 1$, $K(n)$ the $n$th Morava $K$-theory spectrum, $\mathbb{G}_n$ the extended Morava stabilizer group, and $K(A)$ the algebraic $K$-theory spectrum of a commutative $S$-algebra $A$. For a type $n+1$ complex $V_n$, Ausoni and Rognes conjectured that (a) the unit map $i_n: L_{K(n)}(S^0) \to E_n$ from the $K(n)$-local sphere to the Lubin-Tate spectrum induces a map \[K(L_{K(n)}(S^0)) \wedge v_{n+1}^{-1}V_n \to (K(E_n))^{h\mathbb{G}_n} \wedge v_{n+1}^{-1}V_n\] that is a weak equivalence, where (b) since $\mathbb{G}_n$ is profinite, $(K(E_n))^{h\mathbb{G}_n}$ denotes a continuous homotopy fixed point spectrum, and (c) $π_\ast(-)$ of the target of the above map is the abutment of a homotopy fixed point spectral sequence. For $n = 1$, $p \geq 5$, and $V_1 = V(1)$, we give a way to realize the above map and (c), by proving that $i_1$ induces a map \[K(L_{K(1)}(S^0)) \wedge v_{2}^{-1}V_1 \to (K(E_1) \wedge v_{2}^{-1}V_1)^{h\mathbb{G}_1},\] where the target of this map is a continuous homotopy fixed point spectrum, with an associated homotopy fixed point spectral sequence. Also, we prove that there is an equivalence \[(K(E_1) \wedge v_{2}^{-1}V_1)^{h\mathbb{G}_1} \simeq (K(E_1))^{\widetilde{h}\mathbb{G}_1} \wedge v_2^{-1}V_1,\] where $(K(E_1))^{\widetilde{h}\mathbb{G}_1}$ is the homotopy fixed points with $\mathbb{G}_1$ regarded as a discrete group.
