4 citations · 13 across the 12 of their papers we have counts for
19 papers
PCF All The Way Down
Taylor Dupuy, Alon Levy, Thomas Tucker +2
We prove that a finite surjective post-critically finite self-map of a variety in characteristic zero remains post-critically finite on every preperiodic integral effective divisor…
The Dimension Conjecture Implies The Jacobi Bound Conjecture
Taylor Dupuy, David Zureick-Brown
We prove that the Dimension Conjecture implies the Jacobi Bound Conjecture.
The Jacobi Bound Conjecture for Generically Reduced Differential Schemes
Taylor Dupuy, David Zureick-Brown
We prove the Strong Jacobi Bound Conjecture for generically reduced components of differential schemes.
Order one differential equations on nonisotrivial algebraic curves
Taylor Dupuy, James Freitag
In this paper we provide new examples of geometrically trivial strongly minimal differential algebraic varieties living on nonisotrivial curves over differentially closed fields of…
The Theory of the Entire Algebraic Functions
Taylor Dupuy, Ehud Hrushovski
Let A be the integral closure of the ring of polynomials CC[t], within the field of algebraic functions in one variable. We show that A interprets the ring of integers. This contra…
Angle ranks of abelian varieties
Taylor Dupuy, Kiran S. Kedlaya, David Zureick-Brown
Using the formalism of Newton hyperplane arrangements, we resolve the open questions regarding angle rank left over from [DKRV20]. As a consequence we end up generalizing theorems…
Probabilistic Szpiro, Baby Szpiro, and Explicit Szpiro from Mochizuki's Corollary 3.12
Taylor Dupuy, Anton Hilado
In \cite{Dupuy2020a} we gave some explicit formulas for the "indeterminacies" Ind1,Ind2,Ind3 in Mochizuki's Inequality as well as a new presentation of initial theta data. In the p…
The Statement of Mochizuki's Corollary 3.12: Initial Theta Data
Taylor Dupuy, Anton Hilado
We show that Mochizuki's initial theta data is computable from an elliptic curve defined over . We work out the case of initial theta data for the elliptic curve with C…
Counterexamples to a Conjecture of Ahmadi and Shparlinski
Taylor Dupuy, Kiran Kedlaya, David Roe +1
Ahmadi-Shparlinski conjectured that every ordinary, geometrically simple Jacobian over a finite field has maximal angle rank. Using the L-Functions and Modular Forms Database, we p…
Isogeny Classes of Abelian Varieties over Finite Fields in the LMFDB
Taylor Dupuy, Kiran Kedlaya, David Roe +1
This document is intended to summarize the theory and methods behind fq_isog collection inside the ab_var database in the LMFDB as well as some observations gleaned from these data…
Deligne--Illusie Classes as Arithmetic Kodaira--Spencer Classes
Taylor Dupuy, David Zureick-Brown
Faltings showed that "arithmetic Kodaira--Spencer classes" satisfying a certain compatibility axiom cannot exist. By modifying his definitions slightly, we show that the Deligne--I…
Total -differentials on schemes over
Taylor Dupuy, Eric Katz, Joseph Rabinoff +1
For a scheme defined over the length -typical Witt vectors of a characteristic field, we introduce total -differentials which interpolate between Frobeni…
Order one differential equations on nonisotrivial algebraic curves
Taylor Dupuy, James Freitag, Aaron Royer
In this paper we provide new examples of geometrically trivial strongly minimal differential algebraic varieties living on nonisotrivial curves over differentially closed fields of…
A rigid analytic proof that the Abel-Jacobi map extends to compact-type models
Taylor Dupuy, Joseph Rabinoff
Let be a non-Archimedean valued field with valuation ring . Let be a -curve with compact type reduction, so its Jacobian extends to an abelian -scheme .…
Deligne-Illusie Classes I: Lifted Torsors of Lifts of the Frobenius for Curves
Taylor Dupuy
For curves of genus bigger than one we prove that Buium's first arithmetic jet spaces (p-jet spaces) admit the structure of a torsor under some line bundle. This result lifts a kno…
Positivity and Lifts of the Frobenius
Taylor Dupuy
We show that a smooth scheme over a ring of Witt vectors cannot have a lift of the Frobenius if it has positive Kodaira dimension.
Automorphisms of the Affine Line over Nonreduced Rings
Taylor Dupuy
We study automorphisms of the affine line over rings like ZZ/p^n.
Arithmetic differential equations on , III: Galois groups
Alexandru Buium, Taylor Dupuy
Differential equations have arithmetic analogues in which derivatives are replaced by Fermat quotients; these analogues are called arithmetic differential equations and the present…
Arithmetic differential equations on , II: arithmetic Lie theory
Alexandru Buium, Taylor Dupuy
Motivated by the search of a concept of linearity in the theory of arithmetic differential equations we introduce here an arithmetic analogue of Lie algebras and a concept of skew…