7 citations · 19 across the 10 of their papers we have counts for
11 papers
On the elementary theory of the real exponential field
Alessandro Berarducci, Francesco Gallinaro
Assuming Schanuel's conjecture, we prove that the complete theory of the real exponential field is axiomatized by the axioms of definably complete exponential fields sat…
Automorphisms of valued fields: amalgamation and existential closedness
Jan Dobrowolski, Francesco Gallinaro, Rosario Mennuni
We study valued fields equipped with an automorphism. We prove that all of them have an extension admitting an equivariant cross-section of the valuation. In residual characteristi…
Likely intersections in powers of the multiplicative group
Gabriel Andreas Dill, Francesco Gallinaro
We derive two finiteness properties as consequences of the geometrical non-degeneracy of an algebraic subvariety of a power of the multiplicative group, concerning the intersec…
Projective curves and weak second-order logic
Alessandro Berarducci, Francesco Gallinaro
Given an algebraically closed field of characteristic zero, we study the incidence relation between points and irreducible projective curves, or more precisely the poset of irr…
Exponential sums equations and the Exponential Closedness conjecture
Vahagn Aslanyan, Francesco Gallinaro
This is an expository paper aiming to introduce Zilber's Exponential Closedness conjecture to a general audience. Exponential Closedness predicts when (systems of) equations involv…
Dividing Lines between Positive Theories
Anna Dmitrieva, Francesco Gallinaro, Mark Kamsma
We give definitions of the properties OP, IP, -TP, TP, -TP, SOP, SOP and SOP in positive logic, and prove various implications and equivalences between th…
Quasiminimality of complex powers
Francesco Gallinaro, Jonathan Kirby
The complex field, equipped with the multivalued functions of raising to each complex power, is quasiminimal, proving a conjecture of Zilber and providing evidence towards his stro…
The Fundamental theorem of tropical differential algebra over nontrivially valued fields and the radius of convergence of nonarchimedean differential equations
Francesco Gallinaro, Stefano Mereta
We prove a fundamental theorem for tropical partial differential equations, analogous to the fundamental theorem of tropical geometry in this context. We extend results from Aroca…
On Some Systems of Equations in Abelian Varieties
Francesco Gallinaro
We solve a case of the Abelian Exponential-Algebraic Closedness Conjecture, a conjecture due to Bays and Kirby, building on work of Zilber, which predicts sufficient conditions for…
Exponential Sums Equations and Tropical Geometry
Francesco Gallinaro
We show a case of Zilber's Exponential-Algebraic Closedness Conjecture, establishing that the conjecture holds for varieties which split as the product of a linear subspace of the…
Solving Systems of Equations of Raising-to-Powers Type
Francesco Gallinaro
We address special cases of the analogues of the exponential algebraic closedness conjecture relative to the exponential maps of semiabelian varieties and to the modular functi…