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Dieudonné modules and cyclotomic spectra

Banff International Research Station for Mathematical Innovation and Discovery

I will report on joint work with Thomas Nikolaus. We construct a t-structure on the stable infinity-category of cyclotomic spectra and show that the homotopy objects with respect to this t-structure on naturally Dieudonné modules, i.e., abelian groups equipped with operations $V$ and $F$ such that $FV=p$. For smooth schemes over perfect fields of characteristic $p>0$, these cyclotomic homotopy objects are the terms in the de Rhamâ Witt complex. As an application, I will explain how certain formal moduli problems associated to Calabi-Yau varieties admit cyclotomic interpretations, which can be used to strengthen past results about the behavior of these invariants under Fourierâ Mukai equivalence.

Mathematics; Algebraic topology; Category theory; homological algebra

video/mp4

Author affiliation: University of Illinois at Chicago

2019-03-25

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/69192

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/