[ manuscripts ]

  1. Log-Kummer Correspondences and The Third Indeterminacy (with A. Hilado) (Appendix of Interpretation Tables Only -- this may be spun into its expository own document)
  2. The Statement of Mochizuki's Corollary 3.12, Initial Theta Data, and the First Two Indeterminacies, (with A. Hilado)
  3. Probabilistic Szpiro, Baby Szpiro, and Explicit Szpiro from Mochizuki's Corollary 3.12, (with A. Hilado)
  4. Isogeny classes of Abelian Varieties over Finite Fields in the LMFDB, (with K. Kedlaya, D. Roe, and C. Vincent)
  5. Counterexamples to a Conjecture of Ahmadi and Shparlinski (with K. Kedlaya, D. Roe, and C. Vincent)
  6. Deligne-Illusie Classes as Arithmetic Kodaira-Spencer Classes, Journal de Theorie de Nombre de Bordeaux 31, (2019) 371-383 (with D. Zureick-Brown)
  7. Total p-differential on Schemes Over Z/p^2, Journal of Algebra 524, 110-123 (2019) (with E. Katz, J. Rabinoff, and D. Zureick-Brown)
  8. A Rigid Analytic Proof that the Abel-Jacobi map Extends to Compact-Type Models (with J. Rabinoff)
  9. Order One Differential Equations on Non-isotrivial Algebraic Curves (with J. Freitag and A. Royer)
  10. Examples of Geometric Bombieri-Lang-Noguchi Outside of Mordell-Lang: Non-rigid Varieties with Amples but Not Globally Generated Cotangent Bundle, Journal of Number Theory 175 (2017) 158–166
  11. Arithmetic Differential Cocycles on GL_n I: Differential Cocycles (with A. Buium), Journal of Algebra 454, (2016): 273-291
  12. Average Bits of 3^n in Binary, Wieferich primes and a Conjecture of Erdos (with D. Weirich) Journal of Number Theory 158, January (2016): 268-280
  13. Arithmetic Differential Cocycles on GL_n III: Galois theory (with A. Buium), Selecta Mathematica 22 (2), (2016): 529-552
  14. Arithmetic Differential Equations on GL_n, II: Arithmetic Lie-Cartan Theory (with A. Buium), Selecta Mathematica 22 (2), (2016): 447-528
  15. Positivity and Lifts of the Frobenius Math. Res. Lett. 21 (2014) no. 02: 1-7
  16. Lifted Torsors of Lifts of the Frobenius for Curves (Thesis)

[ manuscripts in Limbo ]

  1. The Integers of CC(t)^{alg} Interpret ZZ, (with E. Hrushovski) [Note: Udi went on to extend these results to other fields. Notes are available on request.]
  2. Arithmetic Kolchin Irreducibility (with J. Freitag and L. E. Miller) [Note: for non-affine schemes X the functor A \mapsto X(W(A)) for W the full p-typical witt vector functor is in general not representable (not even by an Algebraic Space). Some work needs to be done on this project to verify this and new ideas are needed. There are some slides on this problem in the talks section of this webpage.]

[ manuscripts not intended for publication ]

  1. Automorphisms of The Affine Line over Non-Reduced Rings

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