Research
Arithmetic geometry and number theory
My work concerns integral and p-adic structures in arithmetic geometry, with particular emphasis on cohomological constructions, arithmetic distributions, and formal groups.
Research themes
Arithmetic geometry and cohomological constructions
Poincaré bundles, Eisenstein and polylogarithmic classes, and their motivic, syntomic, de Rham, and étale realizations, with applications to arithmetic invariants and special values.
p-adic Fourier theory and arithmetic distributions
Integral p-adic distributions, Fourier transforms, Hecke correspondences, norm-compatible classes, and their relation to Iwasawa-theoretic constructions and p-adic L-functions.
Formal groups and integral deformation theory
Formal groups, finite subgroup schemes, deformation spaces, and Witt filtrations measuring integral incidence and congruence phenomena. I am also interested in connections with chromatic homotopy theory.
Preprints
Research papers
Integral trace duality and the Witt filtration on Lubin–Tate space
Andrea Taccani, 2026. arXiv:2610.18246.
The paper identifies Rezk's Witt filtration with the divisibility filtration of integral trace pairings on subgroup algebras. It derives a recursion for the filtration, computes the cokernel of the universal source trace pairing, and studies integral traces along two-step isogeny flags.
Master's thesis · 2026
Poincaré Theta Distributions along Ordinary p-Power Isogenies
My master's thesis studies theta distributions obtained from the Poincaré bundle along ordinary p-power isogenies, together with the underlying biextension geometry, distribution relations, and p-adic integral structures.
Expository notes
Seminar reports and expository material are available on the Notes page.