Non‐integrality of some Steinberg modules
| Autor: | Dan Yasaki, Jeremy Miller, Peter Patzt, Jennifer C. H. Wilson |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
11F75 55N25 55R35 55U10
Pure mathematics Special linear group 01 natural sciences Mathematics - Geometric Topology symbols.namesake Quadratic equation Mathematics::K-Theory and Homology 0103 physical sciences Euclidean geometry FOS: Mathematics Algebraic Topology (math.AT) Mathematics - Algebraic Topology Number Theory (math.NT) 0101 mathematics Mathematics Ring (mathematics) Mathematics - Number Theory Mathematics::Commutative Algebra Group (mathematics) 010102 general mathematics Geometric Topology (math.GT) Imaginary number Cohomology Riemann hypothesis symbols 010307 mathematical physics Geometry and Topology |
| Zdroj: | Journal of Topology. 13:441-459 |
| ISSN: | 1753-8424 1753-8416 |
| DOI: | 10.1112/topo.12132 |
| Popis: | We prove that the Steinberg module of the special linear group of a quadratic imaginary number ring which is not Euclidean is not generated by integral apartments. Assuming the generalized Riemann hypothesis, this shows that the Steinberg module of a number ring is generated by integral apartments if and only if the ring is Euclidean. We also construct new cohomology classes in the top dimensional cohomology group of the special linear group of some quadratic imaginary number rings. Comment: 17 pages. To appear in Journal of Topology |
| Databáze: | OpenAIRE |
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