6 citations · 33 across the 23 of their papers we have counts for
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Golod--Shafarevich for arithmetic surfaces
Timo Keller, Carlo Pagano
We construct Golod--Shafarevich towers of arithmetic surfaces over the integers. In particular, we obtain an arithmetic surface with a section and infinite geometric etale fundamen…
High Rank and Multiplicity in Random and Perfect Profinite Groups
Carlo Pagano, Mark Shusterman
We prove that almost sure topological finite generation holds for a general class of random models of profinite groups. We deduce that in the models introduced by Liu--Wood and Saw…
$\Kab$ has the Bogomolov property for canonical heights
Andrea Ferraguti, Carlo Pagano
We show that for any number field and any rational map in that is not conjugate to a power, (signed) Chebyshev or Lattès map, then has the strong B…
Abelian dynamical Galois groups over global function fields
Andrea Ferraguti, Patrick Ingram, Carlo Pagano
We establish a function field analogue of a recent conjecture of Andrews--Petsche. Our main result characterizes abelian dynamical Galois groups to be precisely the isotrivial ones…
Chowla's non-vanishing conjecture over
Peter Koymans, Carlo Pagano, Mark Shusterman
Let be a prime power. We prove that for 100% of the imaginary quadratic Dirichlet characters of .
Hilbert's tenth problem for finitely generated rings
Peter Koymans, Carlo Pagano
This expository article covers the recent developments surrounding Hilbert's tenth problem for finitely generated rings. We start by recounting the history of Hilbert's tenth probl…