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Harbater, David (1994), "Abhyankar's conjecture on Galois groups over curves",
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Geometrically, the assertion that π is ramified at a finite set
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Abhyankar, Shreeram (1957), "Coverings of
Algebraic Curves",
223:) is defined to be the subgroup generated by all the
388:Comptes Rendus de l'Académie des Sciences, Série I
305:The general case was proved by Harbater, in which
243:is defined as the minimum number of generators of
557:A layman's perspective of Abhyankar's conjecture
179:means that π restricted to the complement of
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203:can be. This is therefore a special type of
115:The question addresses the existence of a
498:Fried, Michael D.; Jarden, Moshe (2008),
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191:. This is in analogy with the case of
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134:as Galois group, and with specified
199:is fixed, and the question is what
138:. From a geometric point of view,
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591:Conjectures that have been proved
357:American Journal of Mathematics
321:can be realised if and only if
262:Raynaud proved the case where
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274:, the conjecture states that
195:. In Abhyankar's conjecture,
142:corresponds to another curve
586:Theorems in abstract algebra
290:+ 1 points, if and only if
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91:of a nonsingular integral
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45:algebraic function fields
543:"Abhyankar's conjecture"
457:Inventiones Mathematicae
414:Inventiones Mathematicae
16:Not to be confused with
70:The problem involves a
205:inverse Galois problem
39:posed in 1957, on the
29:Abhyankar's conjecture
282:, unramified outside
231:for the prime number
239:, and the parameter
100:algebraically closed
469:1994InMat.117....1H
426:1994InMat.116..425R
540:Weisstein, Eric W.
477:10.1007/BF01232232
434:10.1007/BF01231568
384:Serre, Jean-Pierre
149:, together with a
108:of characteristic
37:Shreeram Abhyankar
561:Purdue University
513:978-3-540-77269-9
18:Abhyankar's lemma
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570:Categories
522:1145.12001
485:0805.14014
442:0798.14013
400:0726.14021
341:References
84:, and the
33:conjecture
548:MathWorld
156:Ď€ :
66:Statement
151:morphism
130:), with
465:Bibcode
422:Bibcode
309:is the
266:is the
211:Results
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187:is an
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