Weak Bloch-Beilinson Conjecture for Zero Cycles over p-adic Fields. (joint work with Kanetomo
Cohomological Approaches to Rational Points
March 28,2006 09:30 AM to 10:30 AM
Speakers:
Saito, Shuji
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Abstract: |
Let V be a smooth projective variety over a p-adic field k. Let CH0(V ) be the Chow group
of the zero-cycles on V modulo rational equivalence with A0(V ) CH0(V ), the subgroup of cycle classes of
degree 0. The main theorem of the talk is the following:
Theorem 1: Assume that V has a regular projective flat model X over the ring of integers in k such
that the reduced part of its special fiber is a simple normal crossing divisor on X. Then A0(V ) is the direct
sum of a finite group and the maximal p0-divisible subgroup of A0(V ). Here an abelian group is p0-divisible
if it is divisible by any integer prime to p.
The above theorem is deduced from the following theorem:
Theorem 2: Let X be as above with d + 1 = dim(X). For an integer n > 0 prime to p, the Žetale cycle
map for 1-cycles on the model X
X : CH1(X)/n ! H2d
Žet (X, ”
d
n )
is an isomorphism. |
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Lecture #12271
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