Geodesic
Projective varieties with bad semi-stable reduction at 3 only
Documenta mathematica, Tome 18 (2013), pp. 547-619
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Suppose F=W(k)[1/p] where W(k) is the ring of Witt vectors with coefficients in algebraically closed field k of characteristic p=2. We construct integral theory of p-adic semi-stable representations of the absolute Galois group of F with Hodge-Tate weights from [0,p). This modification of Breuil's theory results in the following application in the spirit of the Shafarevich Conjecture. If Y is a projective algebraic variety over Q with good reduction modulo all primes l=3 and semi-stable reduction modulo 3 then for the Hodge numbers of YC​=Y⊗Q​ C, one has h2(YC​)=h1,1(YC​).
DOI : 10.4171/dm/409
Classification : 11G35, 11S20, 14K15
Mots-clés : p-adic semi-stable representations, Shafarevich conjecture 
@article{10_4171_dm_409,
     author = {Victor Abrashkin},
     title = {Projective varieties with bad semi-stable reduction at 3 only},
     journal = {Documenta mathematica},
     pages = {547--619},
     year = {2013},
     volume = {18},
     doi = {10.4171/dm/409},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/409/}
}
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Victor Abrashkin. Projective varieties with bad semi-stable reduction at 3 only. Documenta mathematica, Tome 18 (2013), pp. 547-619. doi: 10.4171/dm/409

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