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Epimorphisms between finitely generated algebras
Luca Carai, Miriam Kurtzhals, Tommaso Moraschini
https://arxiv.org/abs/2402.14745 https://

Epimorphisms between finitely generated algebras
A quasivariety has the weak ES property when the epimorphisms between its finitely generated members are surjective. A characterization of quasivarieties with the weak ES property is obtained and a method for detecting failures of this property in quasivarieties with a near unanimity term and in congruence permutable varieties is given. It is also shown that under reasonable assumptions the weak ES property implies arithmeticity. In particular, every filtral variety with the weak ES property is…

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This https://arxiv.org/abs/2110.03356 has been replaced.
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$L^2$-type invariants and cohomology jump loci for complex smooth quasi-projective varieties
Let X be a complex smooth quasi-projective variety with a fixed epimorphism $ν\colonπ_1(X)\twoheadrightarrow \mathbb{Z}$. In this paper, we consider the asymptotic behaviour of invariants such as Betti numbers with all possible field coefficients and the order of the torsion part of singular integral homology associated to $ν$, known as the $L^2$-type invariants. At homological degree one, we give concrete formulas for these limits by the geometric information of $X$ when $ν$ is orbifold ef…