论文标题
代数K理论的椭圆形共同学理论
Algebraic K-theory of elliptic cohomology
论文作者
论文摘要
我们计算截短的棕色光谱bp <2>的拓扑环状同源性的MOD（P，V_1，V_2）同质v（2）_* tc（bp <2>），在所有prime p \ ge7中，并表明它是有条理地生成的，免费的F_P [v_3] -modole in 12p+4 Generator， \ le * \ le 2p^3+2p^2+2p-3。在这些Primes Bp <2>是椭圆形的一种形式，我们的结果还确定了其代数K理论的mod（p，v_1，v_2）同拷贝。我们的计算是第一个以精确的定量方式表现出从纯V_2-周期到纯V_3-周期性的色度红移。
We calculate the mod (p, v_1, v_2) homotopy V(2)_* TC(BP<2>) of the topological cyclic homology of the truncated Brown--Peterson spectrum BP<2>, at all primes p\ge7, and show that it is a finitely generated and free F_p[v_3]-module on 12p+4 generators in explicit degrees within the range -1 \le * \le 2p^3+2p^2+2p-3. At these primes BP<2> is a form of elliptic cohomology, and our result also determines the mod (p, v_1, v_2) homotopy of its algebraic K-theory. Our computation is the first that exhibits chromatic redshift from pure v_2-periodicity to pure v_3-periodicity in a precise quantitative manner.
