SCHOOL (AND WORKSHOP) ON
DIOPHANTINE GEOMETRY AND SPECIAL
TRENTO, SEPTEMBER 16-21, 2019
M. Campana (Université
P. Corvaja (Università
degli studi di Udine – It)
A. Turchet (University of Washington – USA)
gianfranco.casnati [nospam] polito.it
The School/Workshop is organized by C. Bertolin, G. Casnati, F.
Galluzzi, R. Notari, F. Vaccarino. For contacting the organizers send a
The School/Workshop is supported by CIRM-Fondazione Bruno Kessler
(formerly CIRM-ITC), Dipartimento di Scienze Matematiche – Politecnico di Torino, Foundation
Journal de Théorie des Nombres de Bordeaux, Dipartimento di
Matematica – Università degli Studi di Torino.
The School and the Workshop will take place at
Fondazione Bruno Kessler-IRST
via Sommarive, 18
38050 Povo (Trento) - Italy
Aim of the School.
The School is mainly aimed to PhD students and young researchers in
Algebraic Geometry, introducing the participants to research, beginning
from a basic level with a view towards the applications and to the most
recent results. A tentative program is as follows.
manifolds: first definition by absence of Bogomolov sheaves of
Specialness vs Weak-specialness.
pairs and their invariants. Multiple fibres. Orbifold base of a
fibration. Bijection between Bogomolov sheaves and fibrations
with orbifold base of general type. Special manifolds: second
definition by absence of fibrations of general type.
orbifold version of Iitaka's Conjecture Cn,m.
Solution when the orbifold base is of general type.
The Core map c, its field of definition. Its conditional decomposition as c=(Jor)n.
Extension of Lang-Vojta's conjectures for
arbitrary smooth projective orbifolds
conjecture: orbifold version. Hyperbolic analogue via Nevanlinna
theory. Solution of Lang's conjectures for some simply-connected
Examples of Weakly-special, but non special threefolds. Description
of their Kobayashi pseudometric.
fundamental group. Abelianity conjecture. Solution for linear
representations. Solution under existence of a Zariski dense entire
curve (after K. Yamanoi). Potential Hilbert Property and specialness.
Hyperbolic analogue (after Corvaja-Zannier).
and integral points. Different notions of integrality, examples.
conjectures, Siegel's and Faltings' Theorems. Algebraic groups, S-unit
Vojta's Main Conjecture. Campana's conjecture, abc
approximation, the Subspace Theorem. Proof of the S-unit
points on curves; a proof of Siegel's theorem. Some applications
to algebraic surfaces.
A more detailed second announcement (containing information on
accomodation, registration and financial supports) will follow probably
January in 2019.