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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.
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
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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
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