Modular Isogeny Complexes
TL;DR: In this paper, a vanishing result on the cohomology of a cochain complex associated to the moduli of chains of finite subgroup schemes on elliptic curves is given.
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Abstract: We describe a vanishing result on the cohomology of a cochain complex associated to the moduli of chains of finite subgroup schemes on elliptic curves. These results have applications to algebraic topology, in particular to the study of power operations for Morava E-theory at height 2.
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Citations
•Posted Content
Rings of power operations for Morava E-theories are Koszul
TL;DR: In this paper, the ring of power operations for any Morava E-theory is shown to be Koszul, and it is shown that the power operation for any Etheory can be reduced to
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Topological modular and automorphic forms
TL;DR: A brief survey of the theory of topological modular forms (TMF) and topological automorphic forms (TAF) can be found in the "Handbook of Homotopy Theory" as mentioned in this paper.
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Spectral Algebra Models of Unstable \(v_n\)-Periodic Homotopy Theory
Mark Behrens,Charles Rezk +1 more
- 28 Aug 2015
TL;DR: A survey of spectral algebra over operads can be found in this paper, where a generalization of Quillen-Sullivan rational homotopy theory is presented, which gives spectral algebra models of unstable (v_n)periodic types.
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•Dissertation
The Lubin-Tate Theory of Spectral Lie Algebras
David Lukas Benjamin Brantner
- 13 May 2017
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The Bousfield-Kuhn functor and topological André-Quillen cohomology
Mark Behrens,Charles Rezk +1 more
TL;DR: In this article, a natural transformation from the Bousfield-Kuhn functor evaluated on a space to the Topological Andre-Quillen cohomology of the K(n)-local Spanier-Whitehead dual of the space is presented.
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References
Arithmetic Moduli of Elliptic Curves. (AM-108), Volume 108
Nicholas M. Katz,Barry Mazur +1 more
- 31 Jan 1985
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Morava E-theory of symmetric groups
TL;DR: In this paper, the authors compute the completed E(n) cohomology of the classifying spaces of the symmetric groups, and relate the answer to the theory of finite subgroups of formal groups.
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Finiteness results for modular curves of genus at least 2
TL;DR: The set of new modular curves over [inline-graphic xmlns:xlink] of genus g is finite and computable, and the computability result is proved an algorithmic version of the de Franchis-Severi Theorem.
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•Posted Content
Morava E-theory of symmetric groups
TL;DR: In this paper, the authors compute the completed E(n) cohomology of the classifying spaces of the symmetric groups, and relate the answer to the theory of finite subgroups of formal groups.
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