منابع مشابه
Relative Support Varieties
We define relative support varieties with respect to some fixed module over a finite dimensional algebra. These varieties share many of the standard properties of classical support varieties. Moreover, when introducing finite generation conditions on cohomology, we show that relative support varieties contain homological information on the modules involved. As an application, we provide a new c...
متن کاملTwisted Support Varieties
We define and study twisted support varieties for modules over an Artin algebra, where the twist is induced by an automorphism of the algebra. Under a certain finite generation hypothesis we show that the twisted variety of a module satisfies Dade’s Lemma and is one dimensional precisely when the module is periodic with respect to the twisting automorphism. As a special case we obtain results o...
متن کاملSupport Varieties for Quantum Groups
Given a root datum (Y,X, . . . ) and an odd integer l G.Lusztig defined a finite-dimensional Hopf algebra u over the cyclotomic field k := Q(ξ) where ξ is a primitive l−th root of unity, see [Lu1]. Suppose that l > h where h is the Coxeter number of the split reductive Lie algebra g over k associated to the root datum (Y,X, . . . ). In this case the cohomology H(u, k) of algebra u with trivial ...
متن کاملWeil Restriction and Support Varieties
This paper extends the comparison results for cohomological support varieties for Chevalley groups of the form G(Fp) established by J. Carlson, Z. Lin, and D. Nakano to Chevalley groups of the form G(Fpd). Other topics considered are complexity and non-maximal support varieties for modules. Techniques developed by J. Pevtsova and the author, together with the use of Weil restriction functors, a...
متن کاملThe Support Problem for Abelian Varieties
Let A be an abelian variety over a number field K. If P and Q are K-rational points of A such that the order of the (mod p) reduction of Q divides the order of the (mod p) reduction of Q for almost all primes (mod p), then there exists a K-endomorphism φ of A and a positive integer k such that kQ = φ(P). In this paper, we solve the support problem for abelian varieties over number fields, thus ...
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ژورنال
عنوان ژورنال: The Quarterly Journal of Mathematics
سال: 2008
ISSN: 0033-5606,1464-3847
DOI: 10.1093/qmath/han032