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PreprintCC BY 4.0arXiv

The Schur multiplier of SL2 and Dedekind zeta-functions over S-integers

  • P. H. Amorim
  • I. V. Picinini
  • B. R. Ramos
  • T. Verissimo
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Abstract

In this paper, we obtain an exact sequence connecting H2(SL2(π’ͺK,S), β„€) to H2(SL2(π’ͺK,T), β„€), where π’ͺK,S is a ring of S-integers and T is a set of primes containing S. We apply this sequence to establish a relation between H2(SL2(π’ͺK,S), β„€) with the second K-group K2(π’ͺK,S), for S large enough. This leads to a description of the rank and size of the torsion of H2(SL2(π’ͺK,S), β„€). As an application, we propose a homological version of the Birch-Tate formula (conjecture) under these assumptions.

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Cite

BibTeXRIS
BibTeX
@misc{amorim2026schur,
  title = {{The Schur multiplier of $\rmSL_2$ and Dedekind zeta-functions over $S$-integers}},
  author = {P. H. Amorim and I. V. Picinini and B. R. Ramos and T. Verissimo},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.28677},
  eprint = {2609.28677},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.28677},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The Schur multiplier of SL_2 and Dedekind zeta-functions over S-integers
AU  - P. H. Amorim
AU  - I. V. Picinini
AU  - B. R. Ramos
AU  - T. Verissimo
PY  - 2026
DA  - 2026/10/02
PB  - arXiv
DO  - 10.48550/arxiv.2609.28677
UR  - https://arxiv.org/abs/2609.28677
AB  - In this paper, we obtain an exact sequence connecting H_2(SL_2(π’ͺ_K,S), β„€) to H_2(SL_2(π’ͺ_K,T), β„€), where π’ͺ_K,S is a ring of S-integers and T is a set of primes containing S. We apply this sequence to establish a relation between H_2(SL_2(π’ͺ_K,S), β„€) with the second K-group K_2(π’ͺ_K,S), for S large enough. This leads to a description of the rank and size of the torsion of H_2(SL_2(π’ͺ_K,S), β„€). As an application, we propose a homological version of the Birch-Tate formula (conjecture) under these assumptions.
ER  -