Strictly commutative realizations of diagrams over the Steenrod algebra and topological modular forms at the prime 2
Tyler Lawson,Niko Naumann +1 more
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In this article, a generalized truncated Brown-Peterson spectrum of chromatic height 2 at the prime 2 was constructed as an E∞-ring spectrum, based on the study of elliptic curves with level-3 structure.Abstract:
Previous work constructed a generalized truncated Brown-Peterson spectrum of chromatic height 2 at the prime 2 as an E∞-ring spectrum, based on the study of elliptic curves with level-3 structure. We show that the natural map forgetting this level structure induces an E∞-ring map from the spectrum of topological modular forms to this truncated Brown-Peterson spectrum, and that this orientation fits into a diagram of E∞-ring spectra lifting a classical diagram of modules over the mod-2 Steenrod algebra. In an appendix we document how to organize Morava’s forms of K-theory into a sheaf of E∞-ring spectra.read more
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On the uniform rectifiability of AD-regular measures with bounded Riesz transform operator: the case of codimension 1
TL;DR: In this article, it was shown that if μ is a d-dimensional Ahlfors-David regular measure, then the boundedness of the Riesz transform in L2(μ) implies that the non-BAUP David-Semmes cells form a Carleson family.
Journal ArticleDOI
Uniform rectifiability, Carleson measure estimates, and approximation of harmonic functions
TL;DR: In this article, the authors acknowledge that the research leading to these results has received funding from the European Research Council under the European Union's Seventh Framework Programme (FP7/2007-2013)/======ERC agreement no. 615112 HAPDEGMT.
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The homology of $\tmf$
TL;DR: In this paper, the mod 2 homology of the spectrum tmf of topological modular forms has been proved by proving a 2-local equivalence t mf ∧ DA(1) ≃ tmmf1(3) ≈ BP 〈2〉, where DA (1) is an eight cell complex whose cohomology doubles the subalgebra A(1), generated by Sq and Sq.
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Rectifiability of harmonic measure
Jonas Azzam,Steve Hofmann,José María Martell,Svitlana Mayboroda,Mihalis Mourgoglou,Xavier Tolsa,Alexander Volberg +6 more
TL;DR: In this article, it was shown that the continuity of the harmonic measure with respect to the Hausdorff measure on E implies that it is rectifiable in the planar case.
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The C2–spectrum Tmf1(3) and its invertible modules
Michael A. Hill,Lennart Meier +1 more
References
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Book
Complex Cobordism and Stable Homotopy Groups of Spheres
TL;DR: An introduction to the homotopy groups of spheres is given in this article, where the Adams spectral sequence and the Adams-Novikov spectral sequence are used to construct the spectral groups.
Book
Rings, Modules, and Algebras in Stable Homotopy Theory
Anthony Elmendorf,Michael Cole +1 more
TL;DR: In this paper, the authors introduce the category of Structured ring and module spectra under $S$ and show how to construct a monadic bar construction on a function spectra.
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Les Schémas de Modules de Courbes Elliptiques
Pierre Deligne,Michael Rapoport +1 more
TL;DR: In this paper, the structure a linfini and the reduction modulo p de X/Γ were studied, where p is the complement of a sous-groupe d'un ensemble fini de points in Riemann compacte.
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Symmetric spectra
TL;DR: In this article, the authors define and study the model category of symmetric spectra, based on simplicial sets and topological spaces, and prove that the category is closed symmetric monoidal.
Book
Morava K-Theories and Localisation
Mark Hovey,Neil P. Strickland +1 more
TL;DR: In this article, the authors define the $E(n)$-local category and the properties of the $K(n)-local category, including smallness and duality.