Cohomology of p-adic Chevalley groups

2025/07/17 by Andrea Dotto, Bao V. Le Hung, Dotto, Andrea +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models

paper · pdf · doi:10.48550/arxiv.2507.13500

Abstract

Let G be a split connected reductive group over the ring of integers of a finite unramified extension K of Q_p. Under a standard assumption on the Coxeter number of G, we compute the cohomology algebra of G(O_K) and its Iwahori subgroups, with coefficients in the residue field of K. Our methods involve a new presentation of some graded Lie algebras appearing in Lazard's theory of saturated p-valued groups, and a reduction to coherent cohomology of the flag variety in positive characteristic. We also consider the case of those inner forms of GL_n(K) that give rise to the Morava stabilizer groups in stable homotopy theory.

Citations

• The mod p cohomology of the Morava stabilizer group at large primes
• Symmetric spectra

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