Lecture 1: Overview

نویسندگان

  • Brian Conrad
  • Sam Lichtenstein
چکیده

Note: The expression for L(s,W ) requires some care, since q v is a complex number acting on a p-adic vector space. What has to be proved is that the characteristic polynomial for the action of Frobv on W i has rational coefficients (and is independent of p), so evaluation using q v makes sense (and the Riemann Hypothesis ensures absolute convergence of the product in a suitable right half-plane depending only in dimX). We conclude from all this that it is a good idea to study L-functions of reasonable p-adic representations. Representation theory can often be used to fill in the bad factors later.

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تاریخ انتشار 2010