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Geometrization of
continuous characters of ℤp×
Clifton Cunningham and Masoud Kamgarpour |
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Vol. 261 (2013), No. 1, 95–99
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Abstract |
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We define the p-adic trace of certain rank-one local systems on the multiplicative group over p-adic numbers, using Sekiguchi and Suwa’s unification of Kummer and Artin–Schreier–Witt theories. Our main observation is that, for every nonnegative integer n, the p-adic trace defines an isomorphism of abelian groups between local systems whose order divides (p − 1)pn and ℓ-adic characters of the multiplicative group of p-adic integers of depth less than or equal to n. |
Keywords
geometrization, character sheaves, continuous
multiplicative characters of p-adic fields, p-adic trace function, continuous
characters of ℤp×
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Mathematical Subject Classification 2010
Primary: 20C15
Secondary: 14G20, 14G15
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Milestones
Received: 14 June 2011
Revised: 14 November 2012
Accepted: 19 November 2012
Published: 28 February 2013
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Authors |
| Clifton Cunningham | |
| Department of Mathematics and
Statistics University of Calgary 2500 University Drive NW Calgary, AB T2N 1N4 Canada |
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| Masoud Kamgarpour | |
| School of Mathematics and
Physics University of Queensland Brisbane, QLD 4072 Australia |
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