arXiv
Open Access
2026
Diagonals and algebraicity modulo $p$: a sharper degree bound
Boris Adamczewski
Alin Bostan
Xavier Caruso
Abstrak
In 1984, Deligne proved that for any prime number $p$, the reduction modulo $p$ of the diagonal of a multivariate algebraic power series with integer coefficients is algebraic over the field of rational functions with coefficients in $\mathbb F_p$. Moreover, he conjectured that the algebraic degrees $d_p$ of these functions should grow at most polynomially in $p$. In this article, we provide a new and elementary proof of Deligne's theorem, which yields the first general polynomial bound on $d_p$ with an explicit and reasonable degree.
Penulis (3)
B
Boris Adamczewski
A
Alin Bostan
X
Xavier Caruso
Akses Cepat
Informasi Jurnal
- Tahun Terbit
- 2026
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