PROJECTIVE GENERATION FOR EQUIVARIANT -MODULES Article Swipe

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Mathematics Equivariant map Affine transformation Pure mathematics Projective variety Variety (cybernetics) Generator (circuit theory) Countable set Discrete mathematics Algebra over a field Power (physics) Physics Statistics Quantum mechanics

Gwyn Bellamy , Sam Gunningham , Sam Raskin ·

YOU? · · 2021 · Open Access · · DOI: https://doi.org/10.1007/s00031-021-09660-1 · OA: W3168335736

We investigate compact projective generators in the category of equivariant "Image missing"-modules on a smooth affine variety. For a reductive group G acting on a smooth affine variety X , there is a natural countable set of compact projective generators indexed by finite dimensional representations of G . We show that only finitely many of these objects are required to generate; thus the category has a single compact projective generator. The proof goes via an analogous statement about compact generators in the equivariant derived category, which holds in much greater generality and may be of independent interest.