, V ) be the Zariski closure of ?. Then: 1. ? n : B n ? B n?1 is a (possibly ramied) Galois cover of smooth proper curves with group 1. The morphism C ? B is separable by Lemma A.2.3.2.1. Then the generator of the Galois group of C ? B is an hyperelliptic involution and so we can apply
, > where i an hyperelliptic involution. Then the proof goes exactly as in
, every U ? C j,n (?) contains ?(n) (resp. ?(?(n + 1))), hence C j
, ? 1)) and use
, By denition of the projective system and induction (and [CT12b, Lemma 3.2] if j = 0
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, ? Yvan André and Mauritz Kerz for accepting refereeing my manuscript
, Hélène Esnault and Javier Fresán for accepting to participate to the jury in the day of the defence
, for having the courage to read some of my drafts, for translating into french Chapter
, for hosting me at RIMS for two summers and for enlightening discussions
, for his innite kindness, for the time he spent in listening and helping me, for all the subtleties of the p-adic machinery that he taught me
, for his innite patience in kindly answering to all my trivial questions
,
, for being almost a mathematical girlfriend, for helping me decoding cryptic papers on overconvergent F-isocrystals and independence, for going crazy on epimorphic subgroup with me for a couple of weeks working on, Chapter
, for being almost a non-mathematical girlfriend, for our travels on foot, by car, train, plane, for almost dying in a beach to see wonderful Greek ruins and in general for being always with me in the last 2 years
, for lending me his shirt the day of my thesis defence, for preparing an amazing breakfast with avocado and eggs, for a number of mathematical (crazy) discussion and for teaching me how to learn without learning
, ? Various people that have participated and/or organized various working groups (even if I don't remember all of them, let me mention some
, for some funny discussion on Galois theory of number elds and because some of the ideas in Chapter 5 arised to me when we were eating an "Hetero classic
, because french bureaucracy can be crazy, but at the Ecole polytechnique everything its easier thanks to her
, Ludovica, for our beers at 18.00, the two British house-mates for teaching me that it's necessary to rinse the dishes, Tommaso and the German girl, for helping me to survive the st couples of months in Paris with a crazy house owner and various problem, ? The two Romans (Elena and Nicola)
, for what we have done (and we will do) together
, for often asking (coherent) mathematical questions, and Matthew, for coming all days in our oce at 11.15 to ask for having lunch
, ? My family (my mother, my father, my sister and my nephew) for their support in all the years of my life