Geometric invariants for non-archimedean semialgebraic sets
Johannes Nicaise
TL;DR
This survey explores how to assign geometric invariants to non-archimedean semialgebraic sets using motivic integration and tropical methods, with applications to refined curve counting.
Contribution
It introduces a comprehensive approach combining motivic integration and tropical geometry to compute invariants of non-archimedean semialgebraic sets, including new applications.
Findings
Geometric invariants can be effectively attached to non-archimedean semialgebraic sets.
Tropical methods facilitate concrete computations of these invariants.
Application to refined curve counting demonstrates practical utility.
Abstract
This survey paper explains how one can attach geometric invariants to semialgebraic sets defined over non-archimedean fields, using the theory of motivic integration of Hrushovski and Kazhdan. It also discusses tropical methods to compute these invariants in concrete cases, as well as an application to refined curve counting, developed in collaboration with Sam Payne and Franziska Schroeter.
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Taxonomy
TopicsPolynomial and algebraic computation · Commutative Algebra and Its Applications · Numerical Methods and Algorithms