Giancarlo LUCCHINI ARTECHE
Associate Professor
Departamento de Matemáticas
Facultad de Ciencias
Universidad de Chile
E-mail: luco @ uchile . cl
Phone: (+56) 2 2978 7305
Address: Departamento de Matemáticas, Facultad de Ciencias, Universidad de Chile, Las Palmeras 3425, Ñuñoa, Santiago, Chile.
Research topics
Algebraic groups, homogeneous spaces, Galois cohomology, rational points, Hasse principle, weak approximation, Brauer groups and Brauer-Manin obstructions.
Recent publications
With Diego Izquierdo. Transfer principles for Galois cohomology and Serre's conjecture II. Accepted in Advances in Mathematics. arXiv
With Charles De Clercq and Mathieu Florence. Lifting vector bundles to Witt vector bundles. Isr. J. Math (published online). arXiv
With Diego Izquierdo. On Kato and Kuzumaki's properties for the Milnor $K_2$ of function fields of $p$-adic curves. Algebra Number Theory 18(4) (2024), 815-846. arXiv
With Mathieu Florence and Diego Izquierdo. On composition of torsors. Int. Math. Res. Not. IMRN 2023(19), 16930-16956. arXiv
Preprints
With Ronan Terpereau. Equivariant automorphism group and real forms of complexity-one varieties. arXiv
With Philippe Gille and Diego Izquierdo. Central simple algebras, Milnor K-theory and homogeneous spaces over complete discretely valued fields of dimension 2. arXiv
With Roberto Díaz. Finite monomial algebras are determined by their automorphism group. arXiv
A note on the unramified Brauer group and local points. pdf
Less recent publications
Le groupe de Brauer non ramifié sur un corps global de caractéristique positive. C. R. Acad. Sci. Paris 351 (2013), 299-302. arXiv
Groupe de Brauer non ramifié des espaces homogènes à stabilisateur fini. J. Algebra 411 (2014), 129-181. arXiv
Approximation faible et principe de Hasse pour des espaces homogènes à stabilisateur fini résoluble. Math. Ann. 360 (2014), 1021-1039. arXiv
Groupe de Brauer non ramifié algébrique des espaces homogènes. Transform. Groups 20 (2015), 463-493. arXiv
With Thomas Budzinski. Un résultat de recherche obtenu grâce à des lycéens. Gaz. Math. 151 (2017), 36-41. arXiv (This is a nice elementary result on finite fields obtained thanks to the work of high-school students during the math tournament TFJM^2)
Weak approximation for homogeneous spaces: reduction to the case with finite stabilizer. Math. Res. Lett. 24(1) (2017), 1-19. arXiv
With Cyril Demarche and Danny Neftin. The Grunwald problem and approximation properties for homogeneous spaces. Ann. Inst. Fourier (Grenoble) 67(3) (2017), 1009-1033. arXiv
Extensions of algebraic groups with finite quotient and non abelian cohomology. J.Algebra 492 (2017), 102-129. arXiv
With Cyril Demarche. Le principe de Hasse pour les espaces homogènes : réduction au cas des stabilisateurs finis. Compos. Math. 155(8) (2019), 1568-1593. arXiv
The unramified Brauer group of homogeneous spaces with finite stabilizer. Trans. Amer. Math. Soc. 372(8) (2019), 5393-5408. arXiv
With Mathieu Florence. On extensions of algebraic groups. Enseign. Math. 65(3/4) (2019), 441-455. arXiv
With Robert Auffarth. Smooth quotients of abelian varieties by finite groups. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) XXI (2020), 673-694. arXiv
With Robert Auffarth and Anita M. Rojas. A decomposition of the Jacobian of a Humbert-Edge curve. In "Geometry at the Frontier: Symmetries and Moduli Spaces of Algebraic Varieties", Contemp. Math. 766 (2021), 31-38. arXiv
With Diego Izquierdo. Local-global principles for homogeneous spaces over some two-dimensional geometric global fields. J. Reine Angew. Math. 781 (2021), 165-186. arXiv
With Robert Auffarth. Smooth quotients of complex tori by finite groups (with an appendix by Stephen Griffeth). Math. Z. 300 (2022), 1071-1091. arXiv
With Luis Arenas-Carmona, Claudio Bravo and Benoit Loisel. Quotients of the Bruhat-Tits tree by arithmetic subgroups of special unitary groups. J. Pure Appl. Algebra 226(8) (2022), 106996. arXiv
With Robert Auffarth and Pablo Quezada. Smooth quotients of abelian surfaces by finite groups that fix the origin. Cubo 24(1) (2022), 37-51. arXiv
With Diego Izquierdo. Homogeneous spaces, algebraic K-theory and cohomological dimension of fields. J. Eur. Math. Soc. 24(6) (2022), 2169-2189. arXiv
With Robert Auffarth. Smooth quotients of principally polarized abelian varieties. Mosc. Math. J. 22(2) (2022), 225-237. arXiv
On homogeneous spaces with finite anti-solvable stabilizers. C. R. Math. Acad. Sci. Paris 360 (2022), 777-780. arXiv
With Álvaro Liendo. Automorphisms of products of toric varieties. Math. Res. Lett. 29(2) (2022), 529-540. arXiv
Postdocs
Gonzalo Manzano-Flores, 2024-2027.
Roberto Díaz, 2023 - 2025.
PhD students
Felipe Rivera (coadvised with Cristián González-Avilés). Ongoing thesis.
Gary Martínez (coadvised with Álvaro Liendo). Two problems on group actions on varieties. Defended on June 25, 2025.
Claudio Bravo (coadvised with Luis Arenas-Carmona). Quotients of the Bruhat-Tits tree by function field analogs of the Hecke congruence subgroups. Defended on March 4, 2022.
Master students
Gabriel Barría. Variedades tóricas completas con grupo de automorfismos semisimple. Defended on June 13, 2025.
Felipe Gambardella. Aproximación débil para espacios homogéneos sobre cuerpos globales geométricos. Defended on January 27, 2022.
Gary Martínez (coadvised with Robert Auffarth). Fibrados asociados a cocientes de variedades abelianas. Defended on March 9, 2021.
Felipe Rivera. Propiedades de aproximación en cohomología galoisiana de grupos finitos. Defended on March 5, 2021.
Pablo Quezada (coadvised with Robert Auffarth). Cocientes suaves de superficies abelianas por grupos finitos. Defended on January 22, 2019.
Seminars
SaNTAS (Santiago Number Theory and Algebra Seminar), which I organized from 2018 to 2024.
Coloquio Las Palmeras, our local Math Department seminar.
Conferences organized
Workshop Agrupando Equipos de Geometría Algebraica 4 (AGREGA 4), January 2025.
XXIV Coloquio Latinoamericano de Álgebra, July 2024.
Workshop Agrupando Equipos de Geometría Algebraica 3 (AGREGA 3), January 2024.
XCI Encuentro Anual de la Sociedad de Matemática de Chile, December 2023
MATH-AmSud School on Geometry: group actions, symmetries, moduli and beyond, December 2023
VI Encuentro Chileno de Teoría de Números, March 2023.
Workshop Agrupando Equipos de Geometría Algebraica 2 (AGREGA 2), February 2023.
IV Latin American School on Algebraic Geometry and its Applications (ELGA IV), December 2019.
V Encuentro Chileno de Teoría de Números, May 2018.
Others
My PhD Thesis : Groupe de Brauer des espaces homogènes à stabilisateur non connexe et applications arithmétiques. Performed under the direction of David Harari. pdf
My Master's Thesis : Abélianisation de la cohomologie galoisienne non abélienne. pdf
Introduction aux Mystères, book by Misha Gromov for which I had the honor of being the chief editor.
