Geodesic
The low-dimensional homology of projective linear group of degree two
Behrooz Mirzaii1 orcid ; Elvis Torres Pérez2 orcid
1Universidade de São Paulo (USP), São Carlos, Brazil
2Pontifical Catholic University of Peru (PUCP), Lima, Peru
Documenta mathematica, Tome 30 (2025) no. 5, pp. 1157-1199

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In this article we study the low-dimensional homology of the projective linear group PGL2​(A) over a commutative ring A. In particular, we prove a Bloch–Wigner type exact sequence over local domains. As application we prove that
DOI : 10.4171/dm/1014
Classification : 19D55, 20J06
Mots-clés : projective linear group, K-groups, Steinberg symbols, homology of groups

Behrooz Mirzaii  1   ; Elvis Torres Pérez  2

1 Universidade de São Paulo (USP), São Carlos, Brazil
2 Pontifical Catholic University of Peru (PUCP), Lima, Peru 
Behrooz Mirzaii; Elvis Torres Pérez. The low-dimensional homology of projective linear group of degree two. Documenta mathematica, Tome 30 (2025) no. 5, pp. 1157-1199. doi: 10.4171/dm/1014
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     title = {The low-dimensional homology of projective linear group of degree two},
     journal = {Documenta mathematica},
     pages = {1157--1199},
     year = {2025},
     volume = {30},
     number = {5},
     doi = {10.4171/dm/1014},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/1014/}
}
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