ترغب بنشر مسار تعليمي؟ اضغط هنا

Gross-Hopkins Duals of Higher Real K-theory Spectra

394   0   0.0 ( 0 )
 نشر من قبل Agnes Beaudry
 تاريخ النشر 2017
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

We determine the Gross-Hopkins duals of certain higher real $K$-theory spectra. More specifically, let $p$ be an odd prime, and consider the Morava $E$-theory spectrum of height $n=p-1$. It is known, in the expert circles, that for certain finite subgroups $G$ of the Morava stabilizer group, the homotopy fixed point spectra $E_n^{hG}$ are Gross-Hopkins self-dual up to a shift. In this paper, we determine the shift for those finite subgroups $G$ which contain $p$-torsion. This generalizes previous results for $n=2$ and $p=3$.



قيم البحث

اقرأ أيضاً

We investigate topological T-duality in the framework of non-abelian gerbes and higher gauge groups. We show that this framework admits the gluing of locally defined T-duals, in situations where no globally defined (geometric) T-duals exists. The glu ing results into new, higher-geometrical objects that can be used to study non-geometric T-duals, alternatively to other approaches like non-commutative geometry.
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 $MU_{mathbb{R}}$.
98 - Hana Jia Kong 2020
We construct a $C_2$-equivariant spectral sequence for RO$(C_2)$-graded homotopy groups. The construction is by using the motivic effective slice filtration and the $C_2$-equivariant Betti realization. We apply the spectral sequence to compute the RO $(C_2)$-graded homotopy groups of the completed $C_2$-equivariant connective real $K$-theory spectrum. The computation reproves the $C_2$-equivariant Adams spectral sequence results by Guillou, Hill, Isaksen and Ravenel.
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 present a novel approach to the problem of integrating homotopy Lie algebras by representing the Maurer-Cartan space functor with a universal cosimplicial object. This recovers Getzlers original functor but allows us to prove the existence of addi tional, previously unknown, structures and properties. Namely, we introduce a well-behaved left adjoint functor, we establish functoriality with respect to infinity-morphisms, and we construct a coherent hierarchy of higher Baker-Campbell-Hausdorff formulas. Thanks to these tools, we are able to establish the most important results of higher Lie theory. We use the recent developments of the operadic calculus, which leads us to explicit tree-wise formulas at all stage. We conclude by applying this theory to rational homotopy theory: the left adjoint functor is shown to provide us with homotopy Lie algebra models for topological spaces which faithfully capture their rational homotopy type.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا