Topological modular forms with level structure

DOI10.1007/s00222-015-0589-5zbMath1338.55006arXiv1312.7394OpenAlexW1990495901WikidataQ57444368 ScholiaQ57444368MaRDI QIDQ5963142

Michael A. Hill, Tyler Lawson

Publication date: 4 March 2016

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1312.7394

zbMATH Keywords

logarithmic geometryderived structure sheafelliptic cohomologymoduli of elliptic curvestopological \(q\)-expansionWitten genus

Mathematics Subject Classification ID

Stable homotopy theory, spectra (55P42) Holomorphic modular forms of integral weight (11F11) Elliptic cohomology (55N34) Stacks and moduli problems (14D23)

Related Items (22)

BPS spectra and invariants for three- and four-manifolds ⋮ Additive decompositions for rings of modular forms ⋮ Simultaneous Kummer congruences and \({\mathbb {E}}_\infty \)-orientations of KO and tmf ⋮ The \(C_2\)-spectrum \(\mathrm{Tmf}_1(3)\) and its invertible modules ⋮ Descent in algebraic \(K\)-theory and a conjecture of Ausoni-Rognes ⋮ Odd primary analogs of real orientations ⋮ Detecting and describing ramification for structured ring spectra ⋮ Lifting \(N_\infty\) operads from conjugacy data ⋮ Connective models for topological modular forms of level \(n\) ⋮ The telescope conjecture at height 2 and the tmf resolution ⋮ Local Gorenstein duality in chromatic group cohomology ⋮ Topological modular forms and the absence of all heterotic global anomalies ⋮ Ausoni-Bökstedt duality for topological Hochschild homology ⋮ Codes, vertex operators and topological modular forms ⋮ Obstruction theory and the level n elliptic genus ⋮ ELLIPTIC COHOMOLOGY IS UNIQUE UP TO HOMOTOPY ⋮ Characteristic classes in $TMF$ of level $\Gamma _1(3)$ ⋮ Rings of modular forms and a splitting of \(\mathrm{TMF}_0(7)\) ⋮ The Hecke algebra action and the Rezk logarithm on Morava E-theory of height 2 ⋮ 4-manifolds and topological modular forms ⋮ Affineness and chromatic homotopy theory ⋮ Topological modular forms with level structure: Decompositions and duality

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Power operations in orbifold Tate \(K\)-theory
• Duality for topological modular forms
• \(K(1)\)-local topological modular forms
• Elliptic genera, modular forms over \(KO_ *\), and the Brown-Kervaire invariant
• Forms of K-theory
• \(K\)-theory of log-schemes. I.
• Topological modular forms of level 3
• Elliptic curves and modular forms in algebraic topology. Proceedings of a conference held at the Institute for Advanced Study, Princeton, NJ, Sept. 15-17, 1986
• Higher congruences between modular forms
• Hecke operators as operations in elliptic cohomology
• Presheaves of symmetric spectra
• Elliptic spectra, the Witten genus and the theorem of the cube
• Model structures on commutative monoids in general model categories
• Residues and duality. Lecture notes of a seminar on the work of A. Grothendieck, given at Havard 1963/64. Appendix: Cohomology with supports and the construction of the \(f^!\) functor by P. Deligne
• Strictly Commutative Realizations of Diagrams Over the Steenrod Algebra and Topological Modular Forms at the Prime 2
• Realizing Families of Landweber Exact Homology Theories
• Commutativity conditions for truncated Brown-Peterson spectra of height 2
• Realizability of algebraic Galois extensions by strictly commutative ring spectra
• The construction of 𝑡𝑚𝑓
• From elliptic curves to homotopy theory
• 𝐾(1)-local 𝐸_{∞}-ring spectra
• Topological automorphic forms
• The Arithmetic of Elliptic Curves
• A Survey of Elliptic Cohomology
• Arithmetic Moduli of Elliptic Curves. (AM-108)
• Logarithmic structures of Fontaine-Illusie. II
• Operads and Γ-homology of commutative rings
• Hypercovers and simplicial presheaves
• Power operations in elliptic cohomology and representations of loop groups
• Lectures on Logarithmic Algebraic Geometry
• Symmetric spectra
• Les Schémas de Modules de Courbes Elliptiques
• The sigma orientation is an H [infinity map]
• Affineness and chromatic homotopy theory
• Buildings, elliptic curves, and the K (2)-local sphere
• Computing Weight One Modular Forms over $\mathbb{C}$ and $\overline{\mathbb{F}}_{p}$
• Higher Topos Theory (AM-170)
• On the formal group laws of unoriented and complex cobordism theory

This page was built for publication: Topological modular forms with level structure