Use this URL to cite or link to this record in EThOS:  https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.565349 
Title:  Prol fundamental groups of generically ordinary semistable fibrations with low slope  
Author:  D'Lima, M. 
ISNI:
0000 0004 2730 3693


Awarding Body:  University College London (University of London)  
Current Institution:  University College London (University of London)  
Date of Award:  2011  
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Abstract:  
Let k be an algebraically closed field of characteristic p > 0 and l a prime that is distinct from p. Let f : S \rightarrow C be a generically ordinary, semistable fibration of a projective smooth surface S to a projective smooth curve C over k. Let F be a general fibre of f, which is a smooth curve of genus g \geq 2. We assume that f is generically strongly lordinary, by which we mean that every cyclic etale covering of degree l of the generic fibre of f is ordinary. Suppose that f is not locally trivial and is relatively minimal. Then deg f*\omegaS/C > 0, where \omegaS/C is the sheaf associated to the relative canonical divisor KS/C = KS − f*KC. Hence the slope of f,\lambda( f ) = K2 S/C/deg f*\omegaS/C is welldefined. Consider the pushout square \pi1(F) \rightarrow \pi1(S) \rightarrow \Pi(C) \rightarrow 1 \downarrow \Pi where \pi1 is the algebraic fundamental group and \pil1 is the prol fundamental group. When f is nonhyperelliptic and \lambda(f) < 4, we show that the morphism \pil1(F)\rightarrow /alpha\Pi is trivial.


Supervisor:  Not available  Sponsor:  Not available  
Qualification Name:  Thesis (Ph.D.)  Qualification Level:  Doctoral  
EThOS ID:  uk.bl.ethos.565349  DOI:  Not available  
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