VORONOI COMPLEXES IN HIGHER DIMENSIONS, COHOMOLOGY OF $GL_N (Z)$ FOR $N\ge 8$ AND THE TRIVIALITY OF $K_8 (Z)$
| Autor: | Dutour Sikiric, Mathieu, Elbaz-Vincent, Philippe, Kupers, Alexander, Martinet, Jacques |
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| Přispěvatelé: | Rudjer Boskovic Institute [Zagreb], Institut Fourier (IF ), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Department of Mathematics [Cambridge] (HARVARD), Harvard University [Cambridge], Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), ANR-15-IDEX-0002,UGA,IDEX UGA(2015), Rudjer Boskovic Institute, Institut Fourier (IF), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA), ANR-15-IDEX-02,CYBER@ALPS,Grenoble Alpes Cybersecurity Institute(2017) |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Kummer-Vandiver conjecture
Voronoi complex group cohomology modular groups well-rounded lattices Perfect forms [MATH.MATH-KT]Mathematics [math]/K-Theory and Homology [math.KT] Steinberg modules linear programming arithmetic groups K-theory of integers [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT] |
| Popis: | We enumerate the low dimensional cells in the Voronoi cell complexes attached to the modular groups $SL_N (Z)$ and $GL_N (Z)$ for $N = 8, 9, 10, 11$, using quotient sublattices techniques for $N = 8, 9$ and linear programming methods for higher dimensions. These enumerations allow us to compute some cohomology of these groups and prove that $K_8 (Z) = 0$, providing new knowledge on the Kummer-Vandiver conjecture. |
| Databáze: | OpenAIRE |
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