15,889 research outputs found
Linearizing torsion classes in the Picard group of algebraic curves over finite fields
We address the problem of computing in the group of -torsion rational
points of the jacobian variety of algebraic curves over finite fields, with a
view toward computing modular representations.Comment: To appear in Journal of Algebr
The linear space of Betti diagrams of multigraded artinian modules
We study the linear space generated by the multigraded Betti diagrams of
Z^n-graded artinian modules of codimension n whose resolutions become pure of a
given type when taking total degrees. We show that the multigraded Betti
diagram of the equivariant resolution constructed by D.Eisenbud, J.Weyman, and
the author, and all its twists, form a basis for this linear space.Comment: 15 pages, some modifications and added materia
Explicit form of Cassels' -adic embedding theorem for number fields
In this paper, we mainly give a general explicit form of Cassels' -adic
embedding theorem for number fields. We also give its refined form in the case
of cyclotomic fields. As a byproduct, given an irreducible polynomial over
, we give a general unconditional upper bound for the smallest prime number
such that has a simple root modulo
Criteria for \sigma-ampleness
In the noncommutative geometry of Artin, Van den Bergh, and others, the
twisted homogeneous coordinate ring is one of the basic constructions. Such a
ring is defined by a -ample divisor, where is an automorphism
of a projective scheme X. Many open questions regarding -ample divisors
have remained.
We derive a relatively simple necessary and sufficient condition for a
divisor on X to be -ample. As a consequence, we show right and left
-ampleness are equivalent and any associated noncommutative homogeneous
coordinate ring must be noetherian and have finite, integral GK-dimension. We
also characterize which automorphisms yield a -ample divisor.Comment: 16 pages, LaTeX2e, to appear in J. of the AMS, minor errors corrected
(esp. in 1.4 and 3.1), proofs simplifie
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