Alicia Lima (U Chicago): Anderson duality for even-periodic derived stacks
Nov 18, 2025 11:00 am
Altgeld 243
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- UIUC Math Department
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- In her thesis, Vesna Stojanoska showed that the self-duality of Tmf comes from Grothendieck–Serre duality on the compactified moduli stack of elliptic curves. Her work hints that a six-functor formalism should exist in a derived setting.Recent advances in solid condensed mathematics—especially work of Clausen–Scholze and Mann—make such a formalism for solid quasi-coherent sheaves on derived Deligne–Mumford stacks seem within reach.I will discuss work in progress toward this goal, aiming to reinterpret Anderson duality as a homotopical version of Grothendieck–Serre duality. Proposition 3.15 of Devalapurkar’s The Lubin–Tate Stack and Gross–Hopkins Duality supports this perspective by proving an Anderson-duality statement for even-periodic derived schemes.The objective is to extend this to derived Deligne–Mumford stacks: Specifically, if $f \colon X \to \mathrm{Spec}(S)$ is an even-periodic smooth derived DM stack and $I_{\mathbb{Z}}$ denotes the Anderson dualizing spectrum, then we expect $f^!(I_{\mathbb{Z}}) \in \mathrm{Pic}(X)$, interpreted within the solid condensed setting.