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Transfer ideals and torsion in the Morava \(E\)-theory of abelian groups. (English) Zbl 07217904
Summary: 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.
MSC:
55N22 Bordism and cobordism theories and formal group laws in algebraic topology
55P42 Stable homotopy theory, spectra
55S25 \(K\)-theory operations and generalized cohomology operations in algebraic topology
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