Yves André Explained

Yves André (born December 11, 1959) is a French mathematician, specializing in arithmetic geometry.

Biography

André received his doctorate in 1984 from Pierre and Marie Curie University (Paris VI) with thesis advisor Daniel Bertrand and thesis Structure de Hodge, équations différentielles p-adiques, et indépendance algébrique de périodes d'intégrales abéliennes. He became at CNRS in 1985 a Researcher, in 2000 a Research Director 2nd Class, and in 2009 a Research Director 1st Class (at École Normale Supérieure and Institut de mathématiques de Jussieu – Paris Rive Gauche).^[1]

Research

In 1989, he formulated the one-dimensional-subvariety case of what is now known as the André-Oort conjecture on special subvarieties of Shimura varieties.^[2] Only partial results have been proven so far; by André himself and by Jonathan Pila in 2009. In 2016, André used Scholze's method of perfectoid spaces to prove Melvin Hochster's direct summand conjecture that any finite extension of a regular commutative ring splits as a module.^{[3] [4]}

Awards

In 2011, André received the Prix Paul Doistau–Émile Blutet of the Académie des Sciences. In 2015, he was elected as a Member of the Academia Europaea. He was an invited speaker at the 2018 International Congress of Mathematicians in Rio de Janeiro and gave a talk titled Perfectoid spaces and the homological conjectures.^[5]

Selected publications

• Book: G-Functions and Geometry A Publication of the Max-Planck-Institut für Mathematik, Bonn . Wiesbaden . 1989 . 978-3-663-14108-2 . 860266118 . André . Yves .
• André . Yves . Mumford-Tate groups of mixed Hodge structures and the theorem of the fixed part . Compositio Mathematica . 82 . 1 . 18 October 2022 . 1570-5846 . 1–24 . fr . 22 November 2022.
• Andre . Yves . On the Shafarevich and Tate conjectures for hyperkähler varieties . Mathematische Annalen . Springer Science and Business Media LLC . 305 . 1 . 1996 . 0025-5831 . 10.1007/bf01444219 . 205–248. 122949797 .
• Book: André . Yves . Baldassarri . F. . De Rham cohomology of differential modules on algebraic varieties . Birkhäuser . Basel, Switzerland . 2001 . 978-3-0348-8336-8 . 679321692.
• Period mappings and differential equations. From C to Cp: Tohoku-Hokkaido Lectures in Arithmetic Geometry, Tokyo, Memoirs Mathematical Society of Japan 2003 (with appendix by F. Kato, N. Tsuzuki)
• Web site: Une introduction aux motifs (Motifs purs, motifs mixtes, périodes) . Société Mathématique de France . fr . 22 November 2022.
• Book: André, Yves . Renormalization and Galois Theories . Galois theory, motives and transcendental numbers . IRMA Lectures in Mathematics and Theoretical Physics . 2009 . 15 . 165–177 . European Mathematical Society Publishing House . Zuerich, Switzerland . 10.4171/073-1/4. 978-3-03719-073-9 . 16880343 .
• André . Yves . La conjecture du facteur direct . Publications mathématiques de l'IHÉS . Springer Science and Business Media LLC . 127 . 1 . 7 December 2017 . 0073-8301 . 10.1007/s10240-017-0097-9 . 71–93 . fr. 1609.00345 . 254170253 .

External links

• Web site: YouTube. Yves André - Grothendieck et les équations différentielles. 4 April 2016.
• Web site: YouTube. Yves André - Direct summand conjecture and perfectoid Abhyankar lemma: an overview. 11 November 2016.
• Web site: YouTube. Yves André: What is... a motivic Galois group. 18 January 2018.
• Web site: YouTube. Yves André: Periods of relative 1 motives. 18 January 2018.

Notes and References

1. Web site: Yves André. Academia Europaea.
2. "G-functions and geometry", Vieweg 1989
3. André, Yves. La conjecture du facteur direct. 2016. 1609.00345. math.AG.
4. Bhatt, Bhargav. On the direct summand conjecture and its derived variant. 1608.08882. 2016. math.AG. .
5. André, Yves. Perfectoid spaces and the homological conjectures. 1801.10006. 2018. math.AC.