On the homology of split extensions with $p$–elementary kernel
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- by Marcin Chalupnik PDF
- Proc. Amer. Math. Soc. 129 (2001), 3143-3149 Request permission
Abstract:
We study a Hochschild–Serre spectral sequence associated to a split group extension with kernel $({\mathbf Z/p})^n$. It is shown that a large part of $E^{0*}_2$ must survive to infinity. We also sketch the general procedure of computing this surviving group.References
- Stanislaw Betley, Calculations in $THH$-theory, J. Algebra 180 (1996), no. 2, 445–458. MR 1378539, DOI 10.1006/jabr.1996.0076
- Stanislaw Betley, Stable $K$-theory of finite fields, $K$-Theory 17 (1999), no. 2, 103–111. MR 1696427, DOI 10.1023/A:1007781714000
- C. de Concini and C. Procesi, A characteristic free approach to invariant theory, Advances in Math. 21 (1976), no. 3, 330–354. MR 422314, DOI 10.1016/S0001-8708(76)80003-5
- Leonard Evens and Eric M. Friedlander, On $(K_\ast (\textbf {Z}/p^{2}\textbf {Z})$ and related homology groups, Trans. Amer. Math. Soc. 270 (1982), no. 1, 1–46. MR 642328, DOI 10.1090/S0002-9947-1982-0642328-X
- Thomas G. Goodwillie, Relative algebraic $K$-theory and cyclic homology, Ann. of Math. (2) 124 (1986), no. 2, 347–402. MR 855300, DOI 10.2307/1971283
- Lars Hesselholt and Ib Madsen, On the $K$-theory of finite algebras over Witt vectors of perfect fields, Topology 36 (1997), no. 1, 29–101. MR 1410465, DOI 10.1016/0040-9383(96)00003-1
- Daniel Quillen, On the cohomology and $K$-theory of the general linear groups over a finite field, Ann. of Math. (2) 96 (1972), 552–586. MR 315016, DOI 10.2307/1970825
- Daniel Quillen, Characteristic classes of representations, Algebraic $K$-theory (Proc. Conf., Northwestern Univ., Evanston, Ill., 1976) Lecture Notes in Math., Vol. 551, Springer, Berlin, 1976, pp. 189–216. MR 0578500
- Chih Han Sah, Cohomology of split group extensions, J. Algebra 29 (1974), 255–302. MR 393273, DOI 10.1016/0021-8693(74)90099-4
Additional Information
- Marcin Chalupnik
- Affiliation: Instytut Matematyki, University of Warsaw, ul. Banacha 2, 02–097 Warsaw, Poland
- Email: mchal@mimuw.edu.pl
- Received by editor(s): August 25, 1999
- Received by editor(s) in revised form: March 8, 2000
- Published electronically: April 16, 2001
- Additional Notes: The author was partially supported by the Polish scientific grant (KBN) 2 P03A 01113
- Communicated by: Ralph Cohen
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 3143-3149
- MSC (2000): Primary 20J06
- DOI: https://doi.org/10.1090/S0002-9939-01-05987-1
- MathSciNet review: 1844986