Geodesic
On~homological dimension modulo~$p$
Sbornik. Mathematics, Tome 60 (1988) no. 2, pp. 413-425

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The article provides a construction of an infinite-dimensional compact space of dimension 2 modulo $p$ for any $p$. A characterization of compact spaces $n$-dimensional modulo $p$ in terms of inverse spectrum of polyhedra is given. It is proved that compact spaces $n$-dimensional modulo $p$, and only these spaces, are images of $n$-dimensional compact spaces under maps acyclic in the sense of cohomology with coefficients in $\mathbf Z_p$. Bibliography: 18 titles. 
@article{SM_1988_60_2_a10,
     author = {A. N. Dranishnikov},
     title = {On~homological dimension modulo~$p$},
     journal = {Sbornik. Mathematics},
     pages = {413--425},
     publisher = {mathdoc},
     volume = {60},
     number = {2},
     year = {1988},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1988_60_2_a10/}
}
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A. N. Dranishnikov. On~homological dimension modulo~$p$. Sbornik. Mathematics, Tome 60 (1988) no. 2, pp. 413-425. http://geodesic.mathdoc.fr/item/SM_1988_60_2_a10/