### Research Focus

Algebraic number theory

Most of my research concerns invariants associated with representations of Galois groups of p-adic fields and algebraic number fields. These invariants, though of an arithmetic nature, are related to classical invariants arising in complex algebraic geometry; their study should shed light on geometric aspects of equations over number fields or p-adic fields. Recently, I have studied families of Galois representations depending analytically on p-adic parameters, and how the invariants for such families change with the parameters. Techniques from p-adic analytic function theory and functional analysis have proved useful in this connection.

### Publications

- The Galois theory of the p-adic complex numbers, J. Ramanujan Math. Soc. (2005).
- Galois cohomology and Galois representations, Inventiones Math. (1993).
- An infinite-dimensional Hodge-Tate theory, Bulletin Math. Soc. France (1992).
- The analytic variation of p-adic Hodge structure, Annals of Math. (1988).
- Integral representations associated with p-adic field extensions, Inventiones Math. (1988).
- Lie algebras of Galois groups arising from Hodge-Tate modules, Annals of Math. (1973).