ترغب بنشر مسار تعليمي؟ اضغط هنا

Transfer ideals and torsion in the Morava $E$-theory of abelian groups

97   0   0.0 ( 0 )
 نشر من قبل Nathaniel Stapleton
 تاريخ النشر 2020
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

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.



قيم البحث

اقرأ أيضاً

We construct and study an algebraic theory which closely approximates the theory of power operations for Morava E-theory, extending previous work of Charles Rezk in a way that takes completions into account. These algebraic structures are made explic it in the case of K-theory. Methodologically, we emphasize the utility of flat modules in this context, and prove a general version of Lazards flatness criterion for module spectra over associative ring spectra.
392 - Charles Rezk 2008
Explicit calculations of the algebraic theory of power operations for a specific Morava E-theory spectrum are given, without detailed proofs.
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 islarg ely 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.
60 - Yaping Yang , Gufang Zhao 2021
In this paper, we study a family of new quantum groups labelled by a prime number $p$ and a natural number $n$ constructed using the Morava $E$-theories. We define the quantum Frobenius homomorphisms among these quantum groups. This is a geometric ge neralization of Lusztigs quantum Frobenius from the quantum groups at a root of unity to the enveloping algebras. The main ingredient in constructing these Frobenii is the transchromatic character map of Hopkins, Kuhn, Ravenal, and Stapleton. As an application, we prove a Steinberg-type formula for irreducible representations of these quantum groups. Consequently, we prove that, in type $A$ the characters of certain irreducible representations of these quantum groups satisfy the formulas introduced by Lusztig in 2015.
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