On the cohomology of GL_2 and SL_2 over imaginary quadratic fields
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Soggetti: | |
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| _version_ | 1866911053064962048 |
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| author | Gangl, Herbert Gunnells, Paul E. Hanke, Jonathan Yasaki, Dan |
| author_facet | Gangl, Herbert Gunnells, Paul E. Hanke, Jonathan Yasaki, Dan |
| contents | We report on computations of the cohomology of GL_2(O_D) and SL_2(O_D), where D<0 is a fundamental discriminant. These computations go well beyond earlier results of Vogtmann and Scheutzow. We use the technique of homology of Voronoi complexes, and our computations recover the integral cohomology away from the primes 2, 3. We observed exponential growth in the torsion subgroup of H^2 as $D$ increases, and compared our data to bounds of Rohlfs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_06633 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the cohomology of GL_2 and SL_2 over imaginary quadratic fields Gangl, Herbert Gunnells, Paul E. Hanke, Jonathan Yasaki, Dan Number Theory Rings and Algebras 11F75, 20J06, 11Y99 We report on computations of the cohomology of GL_2(O_D) and SL_2(O_D), where D<0 is a fundamental discriminant. These computations go well beyond earlier results of Vogtmann and Scheutzow. We use the technique of homology of Voronoi complexes, and our computations recover the integral cohomology away from the primes 2, 3. We observed exponential growth in the torsion subgroup of H^2 as $D$ increases, and compared our data to bounds of Rohlfs. |
| title | On the cohomology of GL_2 and SL_2 over imaginary quadratic fields |
| topic | Number Theory Rings and Algebras 11F75, 20J06, 11Y99 |
| url | https://arxiv.org/abs/2308.06633 |