Bloch and Kato ’ s Exponential Map : Three Explicit Formulas
نویسندگان
چکیده
The purpose of this article is to give formulas for BlochKato’s exponential map and its dual for an absolutely crystalline padic representation V , in terms of the (φ,Γ)-module associated to V . As a corollary of these computations, we can give a very simple and slightly improved description of Perrin-Riou’s exponential map, which interpolates Bloch-Kato’s exponentials for the twists of V . This new description directly implies Perrin-Riou’s reciprocity formula. 2000 Mathematics Subject Classification: 11F80, 11R23, 11S25, 12H25, 13K05, 14F30, 14G20
منابع مشابه
2 1 Se p 20 02 BLOCH AND KATO ’ S EXPONENTIAL MAP : THREE EXPLICIT FORMULAS
— The purpose of this article is to give formulas for Bloch-Kato’s exponential map and its dual for an absolutely crystalline p-adic representation V , in terms of the (φ,Γ)module associated to that representation. As a corollary of these computations, we can give a very simple (and slightly improved) description of Perrin-Riou’s exponential map (which interpolates Bloch-Kato’s exponentials for...
متن کاملExplicit Exponential Maps for Hecke Characters at Ordinary Primes
Let E be an elliptic curve with complex multiplication by the ring of integers of an imaginary quadratic field K. The theory of complex multiplication associates E with a Hecke character ψ. The Hasse-Weil Lfunction of E equals the Hecke L-function of ψ, whose special value at s = 1 encodes important arithmetic information of E, as predicted by the Birch and Swinnerton-Dyer conjecture and verifi...
متن کاملA p-adic analogue of the Borel regulator and the Bloch-Kato exponential map
In this paper we define a p-adic analogue of the Borel regulator for the K-theory of p-adic fields. The van Est isomorphism in the construction of the classical Borel regulator is replaced by the Lazard isomorphism. The main result relates this p-adic regulator to the BlochKato exponential and the Soulé regulator. On the way we give a new description of the Lazard isomorphism for certain formal...
متن کاملThe exponential functions of central-symmetric $X$-form matrices
It is well known that the matrix exponential function has practical applications in engineering and applied sciences. In this paper, we present some new explicit identities to the exponential functions of a special class of matrices that are known as central-symmetric $X$-form. For instance, $e^{mathbf{A}t}$, $t^{mathbf{A}}$ and $a^{mathbf{A}t}$ will be evaluated by the new formulas in this par...
متن کاملExponential maps and explicit formulas
In this section we introduce an exponential homomorphism for the Milnor K -groups for a complete discrete valuation field of mixed characteristics. In general, to work with the additive group is easier than with the multiplicative group, and the exponential map can be used to understand the structure of the multiplicative group by using that of the additive group. We would like to study the str...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2003