Homological Algebra Of Semimodules And Semicont... May 2026

The "Semicontinuity" aspect typically refers to the behavior of dimensions (like the rank of a semimodule) under deformations.

This framework provides the "linear algebra" for tropical varieties. Just as homological algebra helps classify manifolds, semimodule homology helps classify and understand the intersections of tropical hypersurfaces. Homological Algebra of Semimodules and Semicont...

A key feature is the adaptation of and Tor functors. Since you cannot always "subtract" to find boundaries, homological algebra here often uses: The "Semicontinuity" aspect typically refers to the behavior

The rank or homological dimension of a semimodule often drops at specific points of a parameter space, mirroring the behavior of coherent sheaves in algebraic geometry. Homological Algebra of Semimodules and Semicont...