| 释义 |
- Definition
- See also
- References
{{distinguish|Tate module}}In mathematics, a Hodge–Tate module is an analogue of a Hodge structure over p-adic fields. {{harvs|txt|last=Serre|year=1967}} introduced and named Hodge–Tate structures using the results of {{harvs|txt|last=Tate|authorlink=John Tate|year=1967}} on p-divisible groups. DefinitionSuppose that G is the absolute Galois group of a p-adic field K. Then G has a canonical cyclotomic character χ given by its action on the pth power roots of unity. Let C be the completion of the algebraic closure of K. Then a finite-dimensional vector space over C with a semi-linear action of the Galois group G is said to be of Hodge–Tate type if it is generated by the eigenvectors of integral powers of χ. See also- p-adic Hodge theory
- Mumford–Tate group
References- {{Citation | last1=Faltings | first1=Gerd | title=p-adic Hodge theory | doi=10.2307/1990970 |mr=924705 | year=1988 | journal=Journal of the American Mathematical Society | issn=0894-0347 | volume=1 | issue=1 | pages=255–299| jstor=1990970 }}
- {{Citation | last1=Serre | first1=Jean-Pierre | author1-link=Jean-Pierre Serre | editor1-last=Springer | editor1-first=Tonny A. | title=Proceedings of a Conference on Local Fields (Driebergen, 1966) | publisher=Springer-Verlag | location=Berlin, New York | isbn=978-3-540-03953-2 |mr=0242839 | year=1967 | chapter=Sur les groupes de Galois attachés aux groupes p-divisibles | pages=118–131}}
- {{Citation | last1=Tate | first1=John T. | editor1-last=Springer | editor1-first=Tonny A. | title=Proc. Conf. Local Fields (Driebergen, 1966) | publisher=Springer-Verlag | location=Berlin, New York | mr=0231827 | year=1967 | chapter=p-divisible groups.}}
{{DEFAULTSORT:Hodge-Tate module}} 3 : Algebraic geometry|Number theory|Hodge theory |