Topological modular forms with level structure: Decompositions and duality

Meier, Lennart

doi:10.1090/tran/8514

Topological modular forms with level structure: Decompositions and duality
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by Lennart Meier PDF

Trans. Amer. Math. Soc. 375 (2022), 1305-1355

Abstract:

Topological modular forms with level structure were introduced in full generality by Hill and Lawson. We will show that these decompose additively in many cases into a few simple pieces and give an application to equivariant $TMF$. Furthermore, we show which $Tmf_1(n)$ are self-Anderson dual up to a shift, both with and without their natural $C_2$-action.

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