Felipe Voloch

from Wikipedia, the free encyclopedia

José Felipe Voloch (born February 13, 1963 in Rio de Janeiro ) is a Brazilian mathematician who deals with arithmetic algebraic geometry and number theory with application in coding theory and cryptography .

Felipe Voloch, Berkeley 1991

Voloch studied at the Instituto de Matemática Pura e Aplicada (IMPA) in Rio de Janeiro with a master's degree in 1982 and received his doctorate in 1985 from JWS Cassels at Cambridge University (Curves over finite fields). He was then assistant professor at IMPA and 1991/92 visiting scholar at the University of California, Berkeley . In 1992 he became Assistant Professor, 1995 Associate Professor and 2000 Professor at the University of Texas at Austin .

Voloch first gave a brief proof of the Mordell conjecture about function fields in characteristic 0 in 1991 (originally proven by Hans Grauert and Yuri Manin in the 1960s). In 1992, with Abramovich, he succeeded in proving the Mordell-Lang conjecture for function fields with characteristic p under a few additional assumptions ( Ehud Hrushovski succeeded in fully proving it using model theory methods).

With Bjorn Poonen in 2006 (published 2010, Annals of Mathematics) he proved a conjecture about the Brauer-Manin obstruction for function bodies (that this is the only obstruction to the Hasse principle , according to which global solvability follows from local solvability).

From 1993 to 1995 he was a Sloan Research Fellow . He is an associate member of the Brazilian Academy of Sciences .

Fonts

  • Diagonal equations over function fields, Boletim da Sociedade Brasileira de Matemática, 19, 1985, 29-39
  • with Karl-Otto Stöhr : Weierstrass points and curves over finite fields, Proc. London Math. Soc., Vol. 52, 1986, pp. 1-19
  • On the conjectures of Mordell and Lang in positive characteristic, Inventiones Mathematicae, 104, 1991, pp. 643-646
  • with Robert F. Coleman : Companion forms and Kodaira-Spencer Theory. Inventiones Mathematicae, 110, 1992, pp. 263-281
  • with Dan Abramovich : Toward a proof of the Mordell-Lang conjecture in positive characteristic, Intern. Math. Research Notices, Vol. 5, 1992, pp. 103-115
  • with Alexandru Buium : Integral points of abelian varieties over function fields of characteristic zero, Mathematische Annalen, Volume 297, 1993, pp. 303-307
  • with Bjorn Poonen: The Brauer-Manin obstruction for subvarieties of abelian varieties over function fields, Annals of Math., 171 (2010), 511-532. Arxiv
  • with Poonen: Random Diophantine Equations, in Poonen, Yuri Tschinkel (editor), Arithmetic of higher dimensional algebraic varieties, Progress in Mathematics 226, Birkhäuser 2004, pp. 175–184
  • Siegel's theorem for complex function fields, Proc. AMS, 121, 1994, 1307
  • Diophantine geometry in characteristic p: a survey, in Fabrizio Catanese (editor) Arithmetic Geometry, Cambridge University Press 1997

Web links

Individual evidence

  1. ↑ José Felipe Voloch. In: abc.org.br. Academia Brasileira de Ciências, accessed August 14, 2019 (Brazilian Portuguese).
  2. ↑ Felipe Voloch in the Mathematics Genealogy Project (English)Template: MathGenealogyProject / Maintenance / id used
  3. ↑ David Harari : Points rationnels sur les sous-variétés des variétés abéliennes au-dessus d'un corps de fonctions, d'après Poonen et Voloch , Séminaire Bourbaki 979, 2006/07
personal data
SURNAME Voloch, Felipe
ALTERNATIVE NAMES Voloch, José Felipe
BRIEF DESCRIPTION Brazilian mathematician
DATE OF BIRTH February 13, 1963
PLACE OF BIRTH Rio de Janeiro