We establish the dynamical Mordell--Lang conjecture over the complex numbers for a family of radially ramified polynomial skew products in arbitrary base dimension and fiber rank. We assume that one fixed iterate sends the vertical critical locus into the invariant zero section. Our result covers affine-linear bases and, under a degree-gap condition, nonlinear \'{e}tale polynomial bases. We also establish a uniform Skolem--Mahler--Lech theorem for a fixed nonlinear orbit and a fixed polynomial-coefficient linear recurrence whose trailing coefficient is a nonzero constant. The theorem applies to joint polynomial and rational relations involving the orbit and finitely many successive terms of any solution. A single eventual period works for every such solution and relation, although the finite exceptional set may depend on the relation. Our proof combines controlled nonarchimedean realizations with an orbitwise transfer theorem for superattracting line-bundle dynamics.
We study numerical comparisons for hypersurface singularities under finite holomorphic maps between smooth germs. We retain Jelonek's topological proof of the Milnor-number inequality in the isolated case and give an algebraic proof using a cyclic factorization, Brieskorn modules, and trace. For a reduced divisor-theor...
Z. Jelonek, V. J. Jorge Pérez, R. A. D. dos Santos· 0 citations
Let $F$ be a non-Archimedean local field of characteristic zero. We prove multiplicity one for every irreducible smooth admissible representation in the split forms of Wan-Zhang Models 6-10. Combining the Gelfand-Kazhdan method with nilpotent-wavefront restrictions on Bernstein-finite equivariant distributions, we esta...
We prove the multivariable Strong Monodromy Conjecture for the local topological zeta function of arbitrary tuples of nonzero nonunit plane curve germs. The entries may be nonreduced and may have common irreducible factors. We also prove that the non-equivariant local motivic and topological zeta functions have the sam...
We prove the automorphic commutator relation conjectured by Liu and Wang arXiv:2504.00275, which is the geometric input for the automorphic Clifford relations in their framework relating higher period integrals to higher derivatives of $L$-functions over function fields. The relation was previously established only und...
We study quiver Demazure algebras through residue covers and root-power quotients. The cover determined by the zero-root subsystem identifies the additive algebra with a finite fixed algebra of Sauter's generalized quiver Hecke construction. Her basis theorem then gives additive PBW in every finite Weyl type, for arbit...
We prove measure-rigidity results for regular polynomial endomorphisms of~$\mathbb{C}^k$. For maps of the same degree whose leading homogeneous parts differ by an invertible linear map on the target, equality of equilibrium measures is equivalent to postcomposition by an affine symmetry of the Julia set. We then show t...
Yu-Gang Zhang· 2 citations
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