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.[3] 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.[4][5]
André, Yves (1989). G-Functions and Geometry A Publication of the Max-Planck-Institut für Mathematik, Bonn. Wiesbaden. ISBN978-3-663-14108-2. OCLC860266118.{{cite book}}: CS1 maint: location missing publisher (link)
Andre, Yves (1996). "On the Shafarevich and Tate conjectures for hyperkähler varieties". Mathematische Annalen. 305 (1). Springer Science and Business Media LLC: 205–248. doi:10.1007/bf01444219. ISSN0025-5831. S2CID122949797.
André, Yves; Baldassarri, F. (2001). De Rham cohomology of differential modules on algebraic varieties. Basel, Switzerland: Birkhäuser. ISBN978-3-0348-8336-8. OCLC679321692.
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)
André, Yves (2009). "Galois theory, motives and transcendental numbers". Renormalization and Galois Theories. IRMA Lectures in Mathematics and Theoretical Physics. Vol. 15. Zuerich, Switzerland: European Mathematical Society Publishing House. pp. 165–177. doi:10.4171/073-1/4. ISBN978-3-03719-073-9. S2CID16880343.