Project description

This project is about the interplay between spectra known from chromatic homotopy theory (topological modular forms, topological automorphic forms, Brown-Peterson spectra) and equivariant homotopy theory. One question of interest to me is how Serre duality from algebraic geometry manifests itself in terms of Anderson duality in topology. This requires in general the use of representation spheres and genuine equivariant homotopy theory. Further directions in this context are Galois extensions of ring spectra, the computation of Picard groups of ring spectra and equivariant elliptic cohomology.

Related publications

Publications

Ben Antieau and Lennart Meier. The Brauer group of the moduli stack of elliptic curves. Algebra & Number Theory, Vol. 14 (2020), No. 9, 2295–2333 arXiv:1608.00851

Lennart Meier and Viktoriya Ozornova. Rings of modular forms and a splitting of \(TMF_0(7)\), Selecta Mathematica (2020) 26:7

Rosona Eldred, Gijs Heuts, Akhil Mathew and Lennart Meier. Monadicity of the Bousfield-Kuhn functor. Proc. Amer. Math. Soc. 147 (2019), 1789-1796 arXiv:1707.05986

John Greenlees and Lennart Meier. Gorenstein duality for Real spectra Algebraic & Geometric Topology 17 (2017), 3547-3619

Mike Hill and Lennart Meier. The \(C_2\)-spectrum \(Tmf_1(3)\) and its invertible modules Algebraic & Geometric Topology 17 (2017) 1953-2011.

Preprints

Lennart Meier. Decomposition results for rings of modular forms. arXiv:1710.03461

Lennart Meier. Topological modular forms with level structures: decompositions and duality. arXiv:1806.06709