Zobrazeno 1 - 10
of 29
pro vyhledávání: '"Dolce, Paolo"'
Autor:
Dolce, Paolo, Tropeano, Francesco
Let's fix a complex abelian scheme $\mathcal A\to S$ of relative dimension $g$, without fixed part, and having maximal variation in moduli. We show that the relative monodromy group $M^{\textrm{rel}}_\sigma$ of a ramified section $\sigma\colon S\to\m
Externí odkaz:
http://arxiv.org/abs/2407.19476
Consider two families of $g$-dimensional abelian varieties induced by two distinct rational maps on the same variety $\overline{\mathcal A}$ onto two bases $\overline S_1$ and $\overline S_2$ and having big common domain of definition. Two non-torsio
Externí odkaz:
http://arxiv.org/abs/2401.07015
Autor:
Dolce, Paolo
Without assuming the Northcott property we provide an upper bound on the number of "big solutions" of a special system of Diophantine inequalities over proper adelic curves. This system is interesting since it is a stronger version Roth's inequality
Externí odkaz:
http://arxiv.org/abs/2308.02998
Autor:
Dolce, Paolo, Mercuri, Pietro
Let $N>1$ be an integer coprime to $6$ such that $N\notin\{5,7,13\}$ and let $g=g(N)$ be the genus of the modular curve $X_0(N)$. We compute the intersection matrices relative to special fibres of the minimal regular model of $X_0(N)$. Moreover we pr
Externí odkaz:
http://arxiv.org/abs/2304.12068
Autor:
Dolce, Paolo, Zucconi, Francesco
We present two possible generalisations of Roth's approximation theorem on proper adelic curves, assuming some technical conditions on the behavior of the logarithmic absolute values. We illustrate how tightening such assumptions makes our inequaliti
Externí odkaz:
http://arxiv.org/abs/2111.12409
Autor:
Dolce, Paolo, Gualdi, Roberto
Publikováno v:
Journal f\"ur die reine und angewandte Mathematik (Crelles Journal), vol. 2022, no. 784, 2022, pp. 131-154
Let $X$ be an arithmetic variety over the ring of integers of a number field $K$, with smooth generic fiber $X_K$. We give a formula that relates the dimension of the first Arakelov-Chow vector space of $X$ with the Mordell-Weil rank of the Albanese
Externí odkaz:
http://arxiv.org/abs/2010.16134
Autor:
Dolce, Paolo
We give an explicit formula for the Deligne pairing for a proper and flat morphisms $f:X\to S$ of schemes, in terms of the determinant of cohomology. The whole construction is justified by an analogy with the intersection theory on non-singular proje
Externí odkaz:
http://arxiv.org/abs/1911.05367
Autor:
Czerniawska, Weronika, Dolce, Paolo
We work with completed adelic structures on an arithmetic surface and justify that the construction under consideration is compatible with Arakelov geometry. The ring of completed adeles is algebraically and topologically self-dual and fundamental ad
Externí odkaz:
http://arxiv.org/abs/1906.03745
Akademický článek
Tento výsledek nelze pro nepřihlášené uživatele zobrazit.
K zobrazení výsledku je třeba se přihlásit.
K zobrazení výsledku je třeba se přihlásit.
Autor:
Dolce, Paolo
Publikováno v:
Kyoto J. Math. 62, no. 2 (2022), 433-470
For an arithmetic surface $X\to B=\operatorname{Spec} O_K$ the Deligne pairing $\left <\,,\,\right > \colon \operatorname{Pic}(X) \times \operatorname{Pic}(X) \to \operatorname{Pic}(B)$ gives the "schematic contribution" to the Arakelov intersection
Externí odkaz:
http://arxiv.org/abs/1812.10834