Research Seminar Algebraic Geometry

Diophantine problems and the $p$-adic period morphism (after Lawrence and Venkatesh)

We will study the new proof of the Mordell conjecture (Faltings’s theorem) recently given by B. Lawrence and A. Venkatesh. This combines methods of number theory, algebraic geometry, complex geometry, and differential geometry/topology. For further details, see the seminar program.

Date: Thursday, 2-4 pm, WSC-N-U-3.05. First meeting: Oct. 18.

Program: pdf


Oct. 18 Introduction U. Görtz
Oct. 25 The Gauss-Manin connection and the complex period morphism F. Gora
Nov. 8 The $p$-adic period morphism and comparison with the complex situation L. Gehrmann
Nov. 15 Galois representations R. Witthaus
Nov. 22 The $S$-unit equation R. Venerucci
Nov. 29 The proof of Mordell’s conjecture: Outline of the strategy and first steps M. Tamiozzo
Dec. 6 Rational points on the base of an abelian-by-finite family M. Würthen
Dec. 13 Construction of the Kodaira-Parshin family H. Zhao
Dec. 20 The Kodaira-Parshin family has full monodromy I L.-C. Lefèvre
Jan. 10 The Kodaira-Parshin family has full monodromy II J. Heinloth
Jan. 17 at 10:15 The Theorem of Bakker and Tsimerman A. Marrama
Jan. 17 Some conjectures on automorphic forms and the cohomology of spaces beyond Shimura varieties P. Scholze (Bonn)
Jan. 24 Higher dimensional cases — /// cancelled ///