2020/03/09 by Alexander B. Ivanov, Ivanov, Alexander B.
Mathematics · Pharmacology, Toxicology and Pharmaceutics · #14F20 (Secondary) #14M15 #20G25 (Primary) #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Alkaloids: synthesis and pharmacology #Combinatorics #Descent (aeronautics) #FOS: Mathematics #Field (mathematics) #Functor #Group (periodic table) #Loop (graph theory) #Loop group #Mathematics #Perfect field #Physics #Pure mathematics #Representation Theory (math.RT) #Surjective function #Topology (electrical circuits) #math.AG #math.RT #msc:14F20 #msc:14M15 #msc:20G25
paper · pdf · doi:10.48550/arxiv.2003.04399
45pages; v3; title changed; introduction rewritten completely; Remark 3.2 added; Proposition 11.9 strengthened; bibiliography updated; minor format changes
openalex publication_date 2020/03/09 · arxiv created 2021/09/03 · arxiv updated 2021/09/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We prove that the perfect loop functor LX of a quasi-projective scheme X over a local non-archimedean field k satisfies arc-descent, strengthening a result of Drinfeld. Then we prove that for an unramified reductive group G, the map LG → L(G/B) is a v-surjection. This gives a mixed characteristic version (for v-topology) of an equal characteristic result (in étale topology) of Bouthier--Česnavičius. In the second part of the article, we use the above results to introduce a well-behaved notion of Deligne--Lusztig spaces Xw(b) attached to unramified p-adic reductive groups. We show that in various cases these sheaves are ind-representable, thus partially solving a question of Boyarchenko. Finally, we show that the natural covering spaces X w(b) are pro-étale torsors over clopen subsets of Xw(b), and analyze some examples.