The epsilon constant conjecture for higher dimensional unramified twists of Z(p)(r)(1)

Bley, Werner und Cobbe, Alessandro (2022): The epsilon constant conjecture for higher dimensional unramified twists of Z(p)(r)(1). In: Canadian Journal of Mathematics - Journal Canadien De Mathematiques, Bd. 74, Nr. 5: S. 1405-1449

Abstract

Let N/K be a finite Galois extension of p-adic number fields, and let rho(nr): G(K) -> Gl(r) (Z(p)) be an r-dimensional unramified representation of the absolute Galois group G(K), which is the restriction of an unramified representation rho(nr)(Qp): G(Qp) -> (Z(p)). In this paper, we consider the Gal( N/K)-equivariant local epsilon-conjecture for the p-adic representation T = Z(p)(r)(1)(rho(nr)). For example, if A is an abelian variety of dimension r defined over Q(p) with good ordinary reduction, then the Tate module T = T-p(A) over cap associated to the formal group A of (A) over cap is a p-adic representation of this form. We prove the conjecture for all tame extensions N/K and a certain family of weakly and wildly ramified extensions N/K. This generalizes previous work of Izychev and Venjakob in the tame case and of the authors in the weakly and wildly ramified case.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Mathematik, Informatik und Statistik > Informatik
• Themengebiete: 000 Informatik, Informationswissenschaft, allgemeine Werke > 004 Informatik
• ISSN: 0008-414X
• Sprache: Englisch