A Life Dedicated to Mathematics

The First Algebra and Number Theory Meeting at UERJ (1st ANTM-UERJ) is organized in celebration of the birthday of Professor Amílcar Pacheco, a Brazilian mathematician whose academic career has been devoted to research and teaching in number theory and arithmetic geometry.

Throughout his career, Professor Pacheco has pursued a wide range of mathematical questions concerning algebraic curves, abelian varieties, function fields, and the arithmetic properties of algebraic varieties. His work reflects the close connections between number theory, algebraic geometry, and Galois theory, and has led to collaborations with researchers at several institutions in Brazil and abroad.

The meeting provides an occasion to celebrate his mathematical career and to bring together colleagues, collaborators, former students, and friends in an atmosphere of scientific exchange and friendship.

Academic Career

Amílcar Pacheco received his Master's degree in Mathematics from the Instituto de Matemática Pura e Aplicada (IMPA) in 1986 and completed his Ph.D. at the same institution in 1989, under the supervision of José Felipe Voloch.

His doctoral research concerned ramified non-Galois coverings of algebraic curves, continuing a line of investigation initiated during his Master's studies on L-functions of cyclic coverings of curves over finite fields.

Following his doctorate, he held a postdoctoral position at Harvard University (1989–1991). He subsequently developed a long academic career in Brazil, including appointments at the Universidade Federal Fluminense (UFF) and the Universidade Federal do Rio de Janeiro (UFRJ).

At UFRJ, where he served from 1995 until his retirement in 2022, he attained the rank of Full Professor of Mathematics. Since 2022, he has been associated with the Universidade do Estado do Rio de Janeiro (UERJ) as a professor.

His international academic activities have included research visits to the Institut de Mathématiques de Jussieu and the Institut Henri Poincaré in Paris, the Mathematical Sciences Research Institute in Berkeley, and the Institute for Advanced Study in Princeton.

During the academic year 2012–2013, he was a senior visiting researcher at the Institut de Mathématiques de Jussieu in Paris, with support from CNPq, CNRS, and the Fondation Sciences Mathématiques de Paris. He was also a senior academic visitor at the University of Oxford in 2017–2018, supported by CAPES.

Mathematical Research

Professor Pacheco's principal research interests lie in number theory and arithmetic geometry, particularly the arithmetic of algebraic curves and abelian varieties over global fields.

His research has addressed fundamental questions concerning rational points, Mordell–Weil groups, Selmer groups, L-functions, and arithmetic invariants of varieties over function fields.

An important part of his work concerns the arithmetic of abelian varieties in positive characteristic. In collaboration with Marc Hindry, he investigated the ranks of Jacobians over function fields and established an analogue of the Brauer–Siegel theorem for abelian varieties in positive characteristic.

Other research directions include the study of rational points on algebraic curves, torsion phenomena in abelian varieties, the arithmetic of Drinfeld modules, and the structure of algebraic fundamental groups of curves.

His collaborations with mathematicians including Marc Hindry, Sinnou David, Fabien Pazuki, Aurélien Galateau, Katherine Stevenson, Pavel Zalesski, and Rania Wazir illustrate the breadth of his mathematical interests and the international character of his research activity.

His publications have appeared in journals such as Journal of Number Theory, Mathematische Annalen, Mathematische Zeitschrift, Acta Arithmetica, Moscow Mathematical Journal, Pacific Journal of Mathematics, and Bulletin de la Société Mathématique de France.

Teaching and Mentorship

Alongside his research activities, Professor Pacheco has made sustained contributions to mathematics education and the supervision of graduate students.

During his career at UFRJ, he taught undergraduate and graduate courses in algebra, algebraic number theory, elliptic curves, commutative algebra, and curves over finite fields.

He has supervised Master's and doctoral research on topics ranging from elliptic curves and the Birch and Swinnerton-Dyer conjecture to Diophantine geometry, modular forms, and arithmetic dynamics.

His commitment to graduate education forms an important part of his academic career, complementing his research contributions and collaborations.

In 2026, he also published the book Álgebra, contributing to the mathematical literature available to Portuguese-speaking students.

An International Mathematical Community

Professor Pacheco's academic trajectory reflects the international nature of modern mathematical research. His collaborations and visits have connected Brazilian mathematical institutions with research groups in Europe and North America.

The participation of researchers from different countries and generations in the First ANTM-UERJ reflects these scientific connections and provides an opportunity for renewed collaboration and discussion.

A Special Celebration at ANTM-UERJ 2026

The conference will include two special activities in honor of Professor Pacheco.

On Tuesday, October 27, the in-person program at UERJ will conclude with a birthday celebration and dinner, bringing together participants, colleagues, and friends.

On Thursday, October 29, the meeting will conclude with an online discussion and tribute to Professor Pacheco, with the participation of Aurélien Galateau.

We are delighted to celebrate this occasion through a scientific meeting that brings together mathematics, friendship, and academic collaboration.

The Organizing Committee of the 1st ANTM-UERJ extends its warmest congratulations and best wishes to Professor Amílcar Pacheco.

Selected Research Publications

1. M. Hindry and A. Pacheco, An Analogue of the Brauer-Siegel Theorem for Abelian Varieties in Positive Characteristic, Moscow Mathematical Journal 16 (2016), 45–93. (Erratum: 22 (2022), 169.)

2. A. Pacheco and A. Galateau, Hauteur et torsion des modules de Drinfeld de rang 2, Journal of Number Theory 179 (2017), 185–219.

3. A. Pacheco and F. Pazuki, Bounds for the number of rational points of curves over function fields, New York Journal of Mathematics 19 (2013), 131–144.

4. A. Pacheco, Selmer groups of abelian varieties in extensions of function fields, Mathematische Zeitschrift 261 (2009), 787–804.

5. A. Pacheco and M. Hindry, Sur le rang des jacobiennes sur un corps de fonctions, Bulletin de la Société Mathématique de France 133 (2005), 275–295.

6. A. Pacheco, M. Hindry, and R. Wazir, Conjectures de Tate et fibrations, Journal of Number Theory 112 (2005), 345–368.

7. A. Pacheco, On the rank of abelian varieties over function fields, Manuscripta Mathematica 118 (2005), 361–381.

8. A. Pacheco, Unramified Galois covers of algebraic curves, Journal of Number Theory 53 (1995), 211–228.

For a more complete record of his publications and academic activities, please consult his Lattes