SoSe 20 Oberseminar: Integral homotopy theory

Time and place: Tuesday 14:15-15:45 online


Given a simply connected topological space, its rational and p-adic homotopy types can be understood in terms of the algebras of its cochains. In more detail, rational homotopy theory, due to Sullivan and Quillen, states that associating to a space its cochain algebra with rational coefficients induces a fully faithful embedding from simply connected rational spaces to rational commutative dgas. Later, an analogous statement for the p-adic case was proved by Mandell, with cdgas replaced by E-infinity-algebras. However, there was no known way to “glue” the information about rational and p-adic cochains together in order to reconstruct the integral homotopy type. In his recent paper Integral models for spaces via the higher Frobenius, Allen Yuan solves this problem by refining the p-adic model, using the Nikolaus–Scholze Frobenius map on E-infinity-rings as one of the main instruments. In this seminar, we will study Yuan’s paper. We will use the language of modern homotopy theory, and the necessary notions from the Nikolaus–Scholze paper will be recalled.

Date Speaker Topic
05.05 Marc Hoyois Overview
12.05 Harry Gindi Tate construction and Tate diagonal
19.05 Marc Hoyois Equivariant stable homotopy theory
26.05 Martin Speirs The E-infinity Frobenius
02.06 Peter Haine Borel global algebras
09.06 Maria Yakerson Partial algebraic K-theory: S-construction
16.06 Denis-Charles Cisinski Partial algebraic K-theory: Q-construction
23.06 Denis Nardin The partial algebraic K-theory of F_p
30.06 Milton Lin The p-complete Frobenius and the action of BN
07.07 George Raptis Integral models for the unstable homotopy category
14.07 Allen Yuan E-infinity coalgebras and a generalized Segal conjecture