Chromatic homotopy is multiplicatively algebraic at large primes

Speaker: Shaul Barkan - Hebrew University of Jerusalem

Abstract: Stable homotopy theory is intimately related to the geometry of formal groups through the Adams Novkiov spectral sequence. Franke took a step towards making this analogy precise by introducing a derived category of certain sheaves on the moduli stack of formal groups as an analog of the $\infty$-category of spectra of chromatic height $\leq h$. He conjectured that at primes sufficiently larger than the height the homotopy truncation of the two categories coincide. Barthel-Schlank-Stapleton proved an asymptotic variant of Franke’s conjecture using categorical ultraproducts. Later, Pstragowski proved an effective yet non-monoidal version of the conjecture. I will discuss work, building on these results, which provides an effective solution to the symmetric monoidal formulation of Franke’s conjecture.