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Singer conjecture for varieties with semismall Albanese map and residually finite fundamental group
Published online by Cambridge University Press: 19 April 2024
Abstract
We prove the Singer conjecture for varieties with semismall Albanese map and residually finite fundamental group.
MSC classification
Primary:
14F45: Topological properties
- Type
- Research Article
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- Copyright
- Copyright © The Author(s), 2024. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh
References
Abert, M., Bergeron, N., Biringer, I. and Gelander, T.. Convergence of normalized Betti numbers in nonpositive curvature. Duke Math. J. 172 (2023), 633–700.CrossRefGoogle Scholar
Avramidi, G., Okun, B. and Schreve, K.. Mod $p$
and torsion homology growth in nonpositive curvature. Invent. Math. 226 (2021), 711–723.CrossRefGoogle Scholar
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240418192759820-0493:S0308210524000520:S0308210524000520_inline134.png?pub-status=live)
Atiyah, M. F.. Elliptic operators, discrete groups and von Neumann algebras. In Colloque ‘Analyse et Topologie’ en l'Honneur de Henri Cartan (Orsay, 1974). Astérisque, vol. 32–33, pp. 43–72 (Paris: Soc. Math. France, 1976).Google Scholar
Beauville, A.. Complex Algebraic Surfaces, 2nd edn. London Mathematical Society Student Texts, vol. 34 (Cambridge: Cambridge University Press, 1996).Google Scholar
Di Cerbo, G. and Di Cerbo, L. F.. On Seshadri constants of varieties with large fundamental group. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 19 (2019), 335–344.Google Scholar
Di Cerbo, L. F. and Lombardi, L.. $L^2$
-Betti numbers and convergence of normalized Hodge numbers via the weak generic Nakano vanishing theorem. Ann. Inst. Fourier (2023), 27. (Online first).Google Scholar
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240418192759820-0493:S0308210524000520:S0308210524000520_inline135.png?pub-status=live)
Di Cerbo, L. F. and Stern, M.. Price inequalities and Betti number growth on manifolds without conjugate points. Commun. Anal. Geom. 30 (2022), 297–334.CrossRefGoogle Scholar
Dodziuk, J.. $L^{2}$
harmonic forms on rotationally symmetric Riemannian manifolds. Proc. Am. Math. Soc. 77 (1979), 395–400.Google Scholar
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240418192759820-0493:S0308210524000520:S0308210524000520_inline136.png?pub-status=live)
Donnelly, H. and Xavier, F.. On the differential form spectrum of negatively curved Riemannian manifolds. Am. J. Math. 106 (1984), 169–185.CrossRefGoogle Scholar
Gromov, M.. Kähler hyperbolicity and $L_2$
-Hodge theory. J. Differ. Geom. 33 (1991), 263–292.CrossRefGoogle Scholar
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240418192759820-0493:S0308210524000520:S0308210524000520_inline137.png?pub-status=live)
Jost, J. and Zuo, K.. Vanishing theorems for $L^2$
-cohomology on infinite coverings of compact Kähler manifolds and applications in algebraic geometry. Commun. Anal. Geom. 8 (2000), 1–30.CrossRefGoogle Scholar
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240418192759820-0493:S0308210524000520:S0308210524000520_inline138.png?pub-status=live)
Lück, W.. Approximating $L^2$
-invariants by their finite-dimensional analogues. Geom. Funct. Anal. 4 (1994), 455–481.CrossRefGoogle Scholar
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240418192759820-0493:S0308210524000520:S0308210524000520_inline139.png?pub-status=live)
Lück, W.. $L^2$
-Invariants: Theory and Applications to Geometry and $K$
-Theory. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics, vol. 44 (Berlin: Springer-Verlag, 2002).Google Scholar
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240418192759820-0493:S0308210524000520:S0308210524000520_inline140.png?pub-status=live)
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240418192759820-0493:S0308210524000520:S0308210524000520_inline141.png?pub-status=live)
Liu, Y., Maxim, L. and Wang, B.. Aspherical manifolds, Mellin transformation and a question of Bobadilla-Kollár. J. Reine Angew. Math. 781 (2021), 1–18.CrossRefGoogle Scholar
Liu, Y., Maxim, L. and Wang, B.. Topology of subvarieties of complex semi-abelian varieties. Int. Math. Res. Not. 14 (2021), 11169–11208.CrossRefGoogle Scholar
Schoen, R. and Yau, S.-T.. Lectures on differential geometry. In Conference Proceedings and Lecture Notes in Geometry and Topology, vol. I (Cambridge, MA: International Press, 1994).Google Scholar