Let <mml:math alttext="$\mathfrak F$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>&#120099;</mml:mi></mml:math> be a one-dimensional Lubin-Tate formal
 group over <mml:math alttext="${\mathbb Z}_p$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>&#8484;</mml:mi><mml:mi>p</mml:mi></mml:msub></mml:mrow></mml:math>. Colmez (1998) and Perrin-Riou (1994) proved an explicit reciprocity
law for tempered distributions  over the formal group
<mml:math alttext="${\mathbb G}_m$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>&#120126;</mml:mi><mml:mi>m</mml:mi></mml:msub></mml:math>. In this paper, the general explicit reciprocity
law over the formal group <mml:math alttext="$\mathfrak F$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>&#120099;</mml:mi></mml:math> is proved.

International Journal of Mathematics and Mathematical Sciences

On explicit reciprocity law over formal groups

Abstract

Copyright