Topological modular forms with level structure

• 成果类型: Article
• 署名作者: Hill, Michael; Lawson, Tyler
• 署名单位: University of Virginia; University of Minnesota System; University of Minnesota Twin Cities
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-015-0589-5
• 发表日期: 2016
• 页码: 359-416
• 关键词: operations

摘要

The cohomology theory known as , for topological modular forms, is a universal object mapping out to elliptic cohomology theories, and its coefficient ring is closely connected to the classical ring of modular forms. We extend this to a functorial family of objects corresponding to elliptic curves with level structure and modular forms on them. Along the way, we produce a natural way to restrict to the cusps, providing multiplicative maps from with level structure to forms of -theory. In particular, this allows us to construct a connective spectrum consistent with properties suggested by Mahowald and Rezk. This is accomplished using the machinery of logarithmic structures. We construct a presheaf of locally even-periodic elliptic cohomology theories, equipped with highly structured multiplication, on the log-,tale site of the moduli of elliptic curves. Evaluating this presheaf on modular curves produces with level structure.