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Yves André

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

Yves André, Oberwolfach 2007

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.[1] 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).[2]

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]

In 2011 André received the Prix Paul Doistau-Émile Blutet of the Académie des Sciences. In 2015 he was elected to Academia Europaea. He was an Invited Speaker with talk Perfectoid spaces and the homological conjectures at the ICM 2018 in Rio de Janeiro.[6]

Selected publications

  • G-functions and geometry: A publication of the Max Planck Institute for Mathematics, Bonn, Aspects of Mathematics, Vieweg 1989
  • Mumford-Tate groups of mixed Hodge structures and the theorem of the fixed part, Composito Mathematica 82(1) 1992, pp, 1–24
  • On the Shafarevich and Tate conjectures for hyperkähler varieties, Mathematische Annalen 305(1) 1996: pp. 205–248 doi:10.1007/BF01444219
  • with Francesco Baldassarri: De Rham cohomology of differential modules on algebraic varieties, Birkhäuser 2001 André, Yves; Baldassarri, Francesco (2012). pbk reprint. ISBN 9783034883368.
  • 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)
  • Une introduction aux motifs, Panoramas et Synthèses 17, SMF 2004
  • Galois theory, motives and transcendental numbers, in: Renormalization and Galois Theory, IRMA Lectures in Math. Theor. Phys. 15, 2009, pp. 165–177

References

  1. ^ Yves André at the Mathematics Genealogy Project
  2. ^ "Yves André". Academia Europaea.
  3. ^ "G-functions and geometry", Vieweg 1989
  4. ^ André, Yves (2016). "La conjecture du facteur direct". arXiv:1609.00345 [math.AG].
  5. ^ Bhatt, Bhargav (2016). "On the direct summand conjecture and its derived variant". arXiv:1608.08882 [math.AG]..
  6. ^ André, Yves (2018). "Perfectoid spaces and the homological conjectures". arXiv:1801.10006 [math.AC].
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