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PROJECTIVE VARIETIES WITH BAD SEMI-STABLE REDUCTION AT 3 ONLY
 

Summary: PROJECTIVE VARIETIES WITH BAD SEMI-STABLE
REDUCTION AT 3 ONLY
VICTOR ABRASHKIN
Abstract. Suppose F = W(k)[1/p] where W(k) is the ring of
Witt vectors with coefficients in algebraicly closed field k of charac-
teristic p = 2. We construct an 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 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, it holds h2
(YC) = h1,1
(YC).
Introduction
Everywhere in the paper p is a fixed prime number, p = 2, k is
an algebraicly closed field of charactersitic p, F is the fraction field of
the ring of Witt vectors W(k), F is a fixed algebraic closure of F and
F = Gal( F/F) is the absolute Galois group of F.
Suppose Y is a projective algebraic variety over Q. Denote by YC

  

Source: Abrashkin, Victor - Department of Mathematical Sciences, University of Durham

 

Collections: Mathematics