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math.AG2023
Arithmetic Deformation of Line Bundles
David Urbanik, Ziquan Yang
We introduce a new method to study mixed characteristic deformation of line bundles. In particular, for sufficiently large smooth projective families $f : \mathscr{X} \to \mathscr{…
math.AG2023
Existence and density of typical Hodge loci
Nazim Khelifa, David Urbanik
Motivated by a question of Baldi-Klingler-Ullmo, we provide a general sufficient criterion for the existence and analytic density of typical Hodge loci associated to a polarizable…
math.AG2023★ 2 cited
Geometric G-functions and Atypicality
David Urbanik
We describe a general method for giving -adic interpretations of -functions arising from degenerating periods of smooth projective algebraic varieties. Using this, we are abl…