2023/10/26 by Pedro F. dos Santos, Santos, Pedro F. dos, Carlos Florentino +3
Mathematics · #14P25 (Primary) 14F45 #55N91 (Secondary) #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2310.17554
openalex publication_date 2023/10/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We obtain a characterization of Maximal and Galois-Maximal C2-spaces (including real algebraic varieties) in terms of RO(C2)-graded cohomology with coefficients in the constant Mackey functor \underlineF2, using the structure theorem of \citeclovermay:structuretheorem. Other known characterizations, for instance in terms of equivariant Borel cohomology, are also rederived from this. For the particular case of a smooth projective real variety V, equivariant Poincaré duality from \citepedro&paulo:quaternionicalgebraiccycles is used to deduce further symmetry restrictions for the decomposition of the RO(C2)-graded cohomology of the complex locus V(C) given by the same structure theorem. We illustrate this result with some computations, including the RO(C2)-graded cohomology with \underlineF2 coefficients of real K3 surfaces.