Geodesic
Projective varieties with bad semi-stable reduction at 3 only
Documenta mathematica, Tome 18 (2013), pp. 547-619.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Suppose $F=W(k)[1/p]$ where $W(k)$ is the ring of Witt vectors with coefficients in algebraically closed field $k$ of characteristic $p\ne 2$. 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 $l\ne 3$ and semi-stable reduction modulo 3 then for the Hodge numbers of $Y_C=Y\otimes _{\Q}\ C$, one has $h^2(Y_C)=h^{1,1}(Y_C)$.
Classification : 11S20, 11G35, 14K15
Keywords: p-adic semi-stable representations, Shafarevich conjecture 
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     author = {Abrashkin, Victor},
     title = {Projective varieties with bad semi-stable reduction at 3 only},
     journal = {Documenta mathematica},
     pages = {547--619},
     publisher = {mathdoc},
     volume = {18},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2013__18__a29/}
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Abrashkin, Victor. Projective varieties with bad semi-stable reduction at 3 only. Documenta mathematica, Tome 18 (2013), pp. 547-619. http://geodesic.mathdoc.fr/item/DOCMA_2013__18__a29/