Work

Hilbert modular forms and p -adic Hodge theory

Year: 2009

Type: article

Abstract: For the p -adic Galois representation associated to a Hilbert modular form, Carayol has shown that, under a certain assumption, its restriction to the local Galois group at a finite place not dividing p is compatible with the local Langlands correspondence. Under the same assumption, we show that the same is true for the places dividing p , in the sense of p -adic Hodge theory, as is shown for an elliptic modular form. We also prove that the monodromy-weight conjecture holds for such representations.

Source: Compositio Mathematica

DOI: 10.1112/s0010437x09004175

Author: Takeshi Saito

Institution: The University of Tokyo

Language: English

Topic: Advanced Algebra and Geometry

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funders: Johns Hopkins University, Japan Society for the Promotion of Science

Awards: Cohomological study of arithmetic varieties, Arithmetic of modularity lifting and Langlands duality, Ramification in arithmetic geometry