Some Contemporary Problems with Origins in the Jugendtraum

By R. Langlands. 2001

47 citations recorded by the source corpus.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/bc9e6a3ca83e1434ac40d37e3611d6d87f75bd2a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. V. Vatsal
2. C. Cornut
3. M. Kisin
4. Georgios Pappas

In Astronomy and Astrophysics

1. V. Vatsal
2. C. Cornut
3. M. Kisin
4. Georgios Pappas

In Geometry and Topology

1. C. Cornut
2. V. Vatsal
3. Georgios Pappas
4. Benjamin Howard
5. M. Kisin
6. T. Gee
7. Keerthi Madapusi Pera
8. Kiran S. Kedlaya

Citations in the corpus

• CM points and quaternion algebras (2005, background): “The latter is described by a conjecture of Langlands [10], proven in [13].”
• Introduction to Shimura Varieties (2004, unknown): “The idea of Langlands and Rapoport (1987) is to give an elementary definition of a category of “fake” abelian varieties (better, abelian motives) over the algebraic closure of a finite field that looks just like the true category, and to describe the points in terms of it.”
• Integral models of Shimura varieties with parahoric level structure (2015, methodology): “One application of such models is to Langlands’ program [46] to compute the Hasse-Weil zeta function of a Shimura variety in terms of automorphic L-functions.”
• Integral models for Shimura varieties of abelian type (2010, methodology): “The problem of constructing smooth models of Shimura varieties was raised by Langlands in his Jugendtraum paper [La] as a (very small) part of his program to describe the zeta function of a Shimura variety in terms of automorphic Lfunctions.”