Some of my recent research interests include:
 

  • Connections between 2-dimensional Arakelov geometry and the new theory of higher adeles on arithmetic surfaces. This is a crucial part of the long term project of generalising Tate's thesis to arithmetic surfaces.
     

  • Diophantine geometry.
     

  • Higher dimensional Arakelov geometry: analogies between classical intersection theory of algebraic varieties  and arithmetic intersection theory.

List of publications and preprints (newest to oldest)*


 

  1. (with F. Zucconi) On the generalisation of Roth's theorem. 
    preprint (2021). PDF (update 09/22)

     

  2. (with R. Gualdi) Numerical equivalence of R-divisors and Shioda-Tate formula for arithmetic varieties.
    Journal für die reine und angewandte Mathematik (Crelle), 784 (2022), pp. 131--154. PDF (update 11/22)

     

  3. Explicit Deligne pairing.
    European Journal of Mathematics, 8, Suppl. 1 (2022), pp. 101--129 . (Journal)

     

  4. (with W. Czerniawska) Adelic geometry on arithmetic surfaces II: completed adeles and idelic Arakelov intersection theory. 
    Journal of Number Theory,  211 (2020),  pp. 235--296. PDF (update 08/21 with a list of notes and errata)
     

  5. Adelic geometry on arithmetic surfaces I: idelic and adelic interpretation of the Deligne pairing.
    Kyoto Journal of Mathematics, 62, 2 (2022),  pp. 433--470. PDF

     

  6. Fields of definition and Belyi type theorems for curves and surfaces.
    New York Journal of Mathematics, 22 (2016), pp. 823--851.  (Journal)



     






*This page contains the most updated versions of the papers, so they may  slightly  vary from the published ones. In most cases the changes involve  typos and misprints, nevertheless when changes are more meaningful a list of errata is provided. 

On  Arxive my papers are not being updated.