11 citations · 20 across the 9 of their papers we have counts for
14 papers
Adic tropicalizations and cofinality of Gubler models
Tyler Foster, Sam Payne
We introduce adic tropicalizations for subschemes of toric varieties as limits of Gubler models associated to polyhedral covers of the ordinary tropicalization. Our main result sho…
Correlations between primes in short intervals on curves over finite fields
Efrat Bank, Tyler Foster
We prove an analogue of the Hardy-Littlewood conjecture on the asymptotic distribution of prime constellations in the setting of short intervals in function fields of smooth projec…
Non-Archimedean and tropical theta functions
Tyler Foster, Joseph Rabinoff, Farbod Shokrieh +1
We define a tropicalization procedure for theta functions on abelian varieties over a non-Archimedean field. We show that the tropicalization of a non-Archimedean theta function is…
Galois actions on analytifications and tropicalizations
Tyler Foster
This paper initiates a research program that seeks to recover algebro-geometric Galois representations from combinatorial data. We study tropicalizations equipped with symmetries c…
Primes in short intervals on curves over finite fields
Efrat Bank, Tyler Foster
We prove an analogue of the Prime Number Theorem for short intervals on a smooth projective geometrically irreducible curve of arbitrary genus over a finite field. A short interval…
Logarithmic Picard groups, chip firing, and the combinatorial rank
Tyler Foster, Dhruv Ranganathan, Mattia Talpo +1
Illusie has suggested that one should think of the classifying group of -torsors on a logarithmically smooth curve over a standard logarithmic point as a logarithmic…
Degenerations of toric varieties over valuation rings
Tyler Foster, Dhruv Ranganathan
We develop a theory of multi-stage degenerations of toric varieties over finite rank valuation rings, extending the Mumford--Gubler theory in rank one. Such degenerations are const…
D-structures and derived Koszul duality for unital operad algebras
Tyler Foster, Po Hu, Igor Kriz
Generalizing a concept of Lipshitz, Ozsváth and Thurs-ton from Bordered Floer homology, we define -structures on algebras of unital operads, which can also be interpreted as a g…
Introduction to adic tropicalization
Tyler Foster
This is an expository article on the adic tropicalization of algebraic varieties. We outline joint work with Sam Payne in which we put a topology and structure sheaf of local topol…
Hahn analytification and connectivity of higher rank tropical varieties
Tyler Foster, Dhruv Ranganathan
We show that the tropicalization of a connected variety over a higher rank valued field is a path connected topological space. This establishes an affirmative answer to a question…
Rational Connectivity and Analytic Contractibility
Morgan Brown, Tyler Foster
Let k be an algebraically closed field of characteristic 0, and let f be a morphism of smooth projective varieties from X to Y over the ring k((t)) of formal Laurent series. We pro…
Higher configuration operads by way of quiver Grassmannians
Tyler Foster
We introduce a construction that associates, to each finite dimensional k-vector space V, a family of projective k-varieties that comes equipped with the structure of a operad in t…
Limits of tropicalizations
Tyler Foster, Philipp Gross, Sam Payne
We give general criteria under which the limit of a system of tropicalizations of a scheme over a nonarchimedean field is homeomorphic to the analytification of the scheme. As an a…
A Noncommutative Version of the Natural Numbers
Tyler Foster
In this note, we construct and study an algebraic system similar to the natural numbers, but with noncommutative addition. The addition we introduce is a binary operation that comm…