ترغب بنشر مسار تعليمي؟ اضغط هنا

A Mini-Course on Morava Stabilizer Groups and Their Cohomology

67   0   0.0 ( 0 )
 نشر من قبل Hans-Werner Henn
 تاريخ النشر 2017
  مجال البحث
والبحث باللغة English
 تأليف Hans-Werner Henn




اسأل ChatGPT حول البحث

The Morava stabilizer groups play a dominating role in chromatic stable ho-motopy theory. In fact, for suitable spectra X, for example all finite spectra, thechromatic homotopy type of X at chromatic level n textgreater{} 0 and a given prime p islargely controlled by the continuous cohomology of a certain p-adic Lie group Gn,in stable homotopy theory known under the name of Morava stabilizer group oflevel n at p, with coefficients in the corresponding Morava module (En)$star$X.



قيم البحث

اقرأ أيضاً

Let $A$ be a finite abelian $p$ group of rank at least $2$. We show that $E^0(BA)/I_{tr}$, the quotient of the Morava $E$-cohomology of $A$ by the ideal generated by the image of the transfers along all proper subgroups, contains $p$-torsion. The proof makes use of transchromatic character theory.
177 - John Nicholson 2019
If $G$ has $4$-periodic cohomology, then D2 complexes over $G$ are determined up to polarised homotopy by their Euler characteristic if and only if $G$ has at most two one-dimensional quaternionic representations. We use this to solve Walls D2 proble m for several infinite families of non-abelian groups and, in these cases, also show that any finite Poincar{e} $3$-complex $X$ with $pi_1(X)=G$ admits a cell structure with a single $3$-cell. The proof involves cancellation theorems for $mathbb{Z} G$ modules where $G$ has periodic cohomology.
235 - Gregory Ginot , Ping Xu 2010
In this paper we study the cohomology of (strict) Lie 2-groups. We obtain an explicit Bott-Shulman type map in the case of a Lie 2-group corresponding to the crossed module $Ato 1$. The cohomology of the Lie 2-groups corresponding to the universal cr ossed modules $Gto Aut(G)$ and $Gto Aut^+(G)$ is the abutment of a spectral sequence involving the cohomology of $GL(n,Z)$ and $SL(n,Z)$. When the dimension of the center of $G$ is less than 3, we compute explicitly these cohomology groups. We also compute the cohomology of the Lie 2-group corresponding to a crossed module $Gto H$ whose kernel is compact and cokernel is connected, simply connected and compact and apply the result to the string 2-group.
329 - Masaki Kameko 2014
For n>2, we prove the mod 2 cohomology of the finite Chevalley group Spin_n(F_q) is isomorphic to that of the classifying space of the loop group of the spin group Spin(n).
In this paper we develop methods for classifying Baker-Richter-Szymiks Azumaya algebras over a commutative ring spectrum, especially in the largely inaccessible case where the ring is nonconnective. We give obstruction-theoretic tools, constructing a nd classifying these algebras and their automorphisms with Goerss-Hopkins obstruction theory, and give descent-theoretic tools, applying Luries work on $infty$-categories to show that a finite Galois extension of rings in the sense of Rognes becomes a homotopy fixed-point equivalence on Brauer spaces. For even-periodic ring spectra $E$, we find that the algebraic Azumaya algebras whose coefficient ring is projective are governed by the Brauer-Wall group of $pi_0(E)$, recovering a result of Baker-Richter-Szymik. This allows us to calculate many examples. For example, we find that the algebraic Azumaya algebras over Lubin-Tate spectra have either 4 or 2 Morita equivalence classes depending on whether the prime is odd or even, that all algebraic Azumaya algebras over the complex K-theory spectrum $KU$ are Morita trivial, and that the group of the Morita classes of algebraic Azumaya algebras over the localization $KU[1/2]$ is $Bbb Z/8 times Bbb Z/2$. Using our descent results and an obstruction theory spectral sequence, we also study Azumaya algebras over the real K-theory spectrum $KO$ which become Morita-trivial $KU$-algebras. We show that there exist exactly two Morita equivalence classes of these. The nontrivial Morita equivalence class is realized by an exotic $KO$-algebra with the same coefficient ring as $End_{KO}(KU)$. This requires a careful analysis of what happens in the homotopy fixed-point spectral sequence for the Picard space of $KU$, previously studied by Mathew and Stojanoska.
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