This question is related to Theory of Strata. Let chi be a multiplicative character of a non-archimedean local field F where v(2)=r(say). Suppose conductor of chi is n. I want to know the last component of the stratum(corresponding to the character) explicitly. More precisely I want to know the structure of the 'unit' involved in the last component.
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1$\begingroup$ Do you mean : the theory of strata as developped by Kutzko and Bushnell ? What do you mean by "v(2) = r" ?! Could explain your notation ? Thanks $\endgroup$– Paul BroussousFeb 2, 2012 at 14:48
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$\begingroup$ yes, it is as developed by Kutzko and Bushnell . v(2) means valuation of 2. I hope now is is self explained. If not, please inform me. -Amiya $\endgroup$– Amiya Kumar MondalFeb 2, 2012 at 16:41
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$\begingroup$ Are you assuming that 2 is a uniformizer of your field F ? Things are definitely not clear ... $\endgroup$– Paul BroussousFeb 2, 2012 at 20:15
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$\begingroup$ No, I am just saying that 2 is ramified in F. One can think of F as a totally ramified extension of Q2(i.e. completion of Q with 2-adic valuation) of degree r. 2 is not uniformizer in F. $\endgroup$– Amiya Kumar MondalFeb 3, 2012 at 7:43
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