An obstruction to lifting schemes to spectral schemes

Speaker(s)

Robert Szafarczyk

Affiliation

University of Copenhagen

Language of the talk

English

Date

March 12, 2025, 10:15 a.m.

Room

room 4070

Seminar

Seminar Algebraic Topology

---

There is a relatively simple purly algebraic obstruction, due to Nikolaus, for lifting commutative rings to the sphere spectrum. As an application, it recovers a classical result on non-existence of fully commutative multiplicative structures on Moore spaces, but is applicable to a much broader set of examples such as number rings. We will generalize this obstruction to schemes. As an example, we show that neither the group scheme G_a nor elliptic curves lift to the sphere spectrum.

---