HodgeTate
The Hodge–Tate theorem is a fundamental result in the arithmetic theory of algebraic varieties and number theory, connecting algebraic geometry with representation theory. It was formulated by William Hodge in the context of complex manifolds and later generalized by John Tate to broader settings, particularly in the study of Galois representations.
The theorem provides a deep relationship between the étale cohomology of varieties over number fields and
In the case of an abelian variety over a number field, the Hodge–Tate theorem asserts that the
The theorem has profound implications for number theory, including the study of modular forms, elliptic curves,