Projective varieties with bad reduction at 3 only

Details Projective varieties with bad reduction at 3 only Projective varieties with bad reduction at 3 only

2010-03-15

arxiv.org/abs/1003.2905v3

Mathematics

Number Theory

68 pages

Scientific paper

Suppose F=W(k)[1/p] where W(k) is the ring of Witt vectors with coefficients in algebraicly 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 Shafarevich's Conjecture. If Y is a projective algebraic variety over the field of rational numbers with good reduction modulo all primes different from 3 and semi-stable reduction modulo 3 then for the Hodge numbers of the complexification Y_C of Y, it holds h^2(Y_C)=h^{1,1}(Y_C).

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