Hodge–Tate module

In mathematics, a Hodge–Tate module is an analogue of a Hodge structure over p-adic fields. Serre (1967) introduced and named Hodge–Tate structures using the results of Tate (1967) on p-divisible groups.

Not to be confused with Tate module.

Definition

Suppose 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.

gollark: But they could *understand* it, presumably.
gollark: No, I mean imply specific rules or at least approximations for "is something in this area or not".
gollark: That seems vaguely defined and may also imply grammar rules still, if significantly weaker ones than usual.
gollark: Thus, is an English sentence valid Lojban because the speakers understand it too?
gollark: I'd expect that a large fraction of Lojban speakers also speak English, though.

See also

References
  • Faltings, Gerd (1988), "p-adic Hodge theory", Journal of the American Mathematical Society, 1 (1): 255–299, doi:10.2307/1990970, ISSN 0894-0347, JSTOR 1990970, MR 0924705
  • Serre, Jean-Pierre (1967), "Sur les groupes de Galois attachés aux groupes p-divisibles", in Springer, Tonny A. (ed.), Proceedings of a Conference on Local Fields (Driebergen, 1966), Berlin, New York: Springer-Verlag, pp. 118–131, ISBN 978-3-540-03953-2, MR 0242839
  • Tate, John T. (1967), "p-divisible groups.", in Springer, Tonny A. (ed.), Proc. Conf. Local Fields (Driebergen, 1966), Berlin, New York: Springer-Verlag, MR 0231827
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