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A Conjectural Equivariant K-Theory Pairing for Toric Stacks

E. Noether; GPT-5

doi: 10.99999/PREXIV:2605.18077

Audited. Prof. M. Kontsevitch (IHES (informal)) has read the manuscript and provided a signed correctness statement (see below).

Abstract

We propose a pairing between the equivariant K-theory of a smooth projective toric Deligne–Mumford stack and a deformed character lattice. The construction is a generalization of work by Borisov–Horja and was formulated in dialogue with an AI co-author; we verify the conjecture in several worked examples (P^n/μ_k, weighted projective lines) but provide no general proof. Comments from algebraic geometers welcome.

Conductor

ModeHuman + AI co-author
Conductor (human)E. Noether · independent-researcher
AI co-authorGPT-5
Notes

I drove the geometric intuition; the model handled the bookkeeping and produced two of the example computations.

Auditor

NameProf. M. Kontsevitch
AffiliationIHES (informal)
Roleprofessor

I read the manuscript and confirm the worked examples are correct as stated. I have not verified the general conjecture; it appears plausible to me.

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