2025/01/16 by Mark Andrea de Cataldo, Siqing Zhang, de Cataldo, Mark Andrea +1
Computer Science · Mathematics · Social Sciences · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Cryptography and Residue Arithmetic #FOS: Mathematics #Historical and Political Studies
paper · pdf · doi:10.48550/arxiv.2501.09850
openalex publication_date 2025/01/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a curve C and a reductive group G in prime characteristic, we relate the de Rham moduli of logarithmic G-connections on C to the Dolbeault moduli of logarithmic G-Higgs bundles on the Frobenius twist of C. We name this result the Log-p-NAHT. It is a logarithmic version of Chen-Zhu's characteristic p Non Abelian Hodge Theorem (p-NAHT). In contrast to the no pole case, the two moduli stacks in the log case are not isomorphic etale locally over the Hitchin base. Instead, they differ by an Artin-Schreier type Galois cover of the base. In contrast to the case over the complex numbers, where some parabolic/parahoric data are needed to specify the boundary behavior of the tame harmonic metrics, no parabolic/parahoric data are needed in Log-p-NAHT. We also establish a semistable version of the Log-p-NAHT, and deduce several geometric and cohomological consequences. In particular, when G=GLr, the Log-p-NAHT induces an embedding of the intersection cohomology of the degree d Dolbeault moduli to that of the degree pd de Rham moduli, and the embedding is an isomorphism when r is coprime to d and p>r.