NTS ABSTRACT: Difference between revisions
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{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20" | {| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20" | ||
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| bgcolor="#F0A0A0" align="center" style="font-size:125%" | ''' | | bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Kiran Kedlaya''' | ||
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| bgcolor="#BCD2EE" align="center" | | | bgcolor="#BCD2EE" align="center" | ''On the algebraicity of (generalized) power series'' | ||
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A remarkable theorem of Christol from 1979 gives a criterion for detecting whether a power series over a finite field of characteristic p represents an algebraic function: this happens if and only if the coefficient of the n-th power of the series variable can be extracted | |||
from the base-p expansion of n using a finite automaton. We will describe a result that extends this result in two directions: we allow | |||
an arbitrary field of characteristic p, and we allow "generalized power series" in the sense of Hahn-Mal'cev-Neumann. In particular, this gives | |||
a concrete description of an algebraic closure of a rational function field in characteristic p (and corrects a mistake in my previous attempt | |||
to give this description some 15 years ago). | |||
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== Sep 10 == | |||
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| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Sean Rostami''' | |||
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| bgcolor="#BCD2EE" align="center" | Fixers of Stable Functionals | |||
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Coming soon... | |||
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Revision as of 02:21, 25 August 2015
Sep 03
| Kiran Kedlaya |
| On the algebraicity of (generalized) power series |
|
A remarkable theorem of Christol from 1979 gives a criterion for detecting whether a power series over a finite field of characteristic p represents an algebraic function: this happens if and only if the coefficient of the n-th power of the series variable can be extracted from the base-p expansion of n using a finite automaton. We will describe a result that extends this result in two directions: we allow an arbitrary field of characteristic p, and we allow "generalized power series" in the sense of Hahn-Mal'cev-Neumann. In particular, this gives a concrete description of an algebraic closure of a rational function field in characteristic p (and corrects a mistake in my previous attempt to give this description some 15 years ago). |
Sep 10
| Sean Rostami |
| Fixers of Stable Functionals |
|
Coming soon... |