Non-archimedean Quantum K-invariants

Abstract: We construct quantum K-invariants in non-archimedean analytic geometry. Our approach differs from the classical one in algebraic geometry via perfect obstruction theory. Instead, we build on our previous works on the foundation of derived non-archimedean geometry, the representability theorem and Gromov compactness. We obtain a list of natural geometric relations between the stacks of stable maps, directly at the derived level, with respect to elementary operations on graphs, namely, products, cutting edges, forgetting tails and contracting edges. They imply immediately the corresponding properties of K-theoretic invariants. The derived approach produces highly intuitive statements and functorial proofs. The flexibility of our derived approach to quantum K-invariants allows us to impose not only simple incidence conditions for marked points, but also incidence conditions with multiplicities. This leads to a new set of enumerative invariants. Our motivations come from non-archimedean enumerative geometry and mirror symmetry. Joint work with M Porta.

algebraic geometry

Audience: researchers in the topic

Derived seminar

Series comments: https://ed-ac-uk.zoom.us/j/89993982042

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