Abstract
This is a quite faithful rendering of a Colloquio De Giorgi I had the honor to give at Scuola Normale Superiore on March 21, 2012. The idea was to explain some open problems in arithmetic algebraic geometry which are simple to state but which remain shrouded in mystery.
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References
T. Barnet-Lamb, D. Geraghty, M. Harris and R. Taylor, A family of Calabi-Yau varieties and potential automorphy II, Publ. Res. Inst. Math. Sci. 47 (2011), 29–98.
L. Clozel, M. Harris and R. Taylor, Automorphy for some ℓ-adic Lifts of Automorphic mod ℓ Galois Representations, with Appendix A, summarizing unpublished work of Russ Mann, and Appendix B by Marie-France Vignéras, Publ. Math. Inst. Hautes Études Sci. 108 (2008), 1–181.
R. Coleman, On the Galois groups of the exponential Taylor polynomials, Enseign. Math. 33 (1987), 183–189.
W. Feller, “An Introduction to Probability Theory and its Applications”, Vol. II, John Wiley and Sons, 1966.
F. Fité, K. Kedlaya, V. Rotger and A. Sutherland, Sato-Tate distributions and Galois endomorphism modules in genus 2, Compos. Math. 148 (2012), 1390–1442.
M. Harris, N. Shepherd-Barron and R. Taylor, A family of Calabi-Yau varieties and potential automorphy, Ann. of Math. 171 (2010), 779–813.
H. Osada, The Galois groups of the polynomials X n + aX ℓ + b, J. Number Th. 25 (1987), 230–238.
J.-P. Serre, “Abelian ℓ-adic Representations”, Addison-Wesley, 1989.
R. Taylor, Automorphy for some ℓ-adic lifts of automorphic modℓ Galois representations, II, Publ. Math. Inst. Hautes Études Sci. 108 (2008), 183–239.
Andé Weil, “Variétés abéliennes et courbes algébriques”, Actualités Sci. Ind., no. 1064, Publ. Inst. Math. Univ. Strasbourg 8 (1946), Hermann & Cie., Paris, 1948. 165 pp.
Yuri G. Zarhin, Very simple 2-adic representations and hyperelliptic Jacobians, Mosc. Math. J. 2 (2002), 403–431.
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Katz, N.M. (2013). Simple things we don’t know. In: Zannier, U. (eds) Colloquium De Giorgi 2010–2012. Publications of the Scuola Normale Superiore, vol 4. Edizioni della Normale, Pisa. https://doi.org/10.1007/978-88-7642-457-1_2
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DOI: https://doi.org/10.1007/978-88-7642-457-1_2
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