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Freyd's generating hypothesis, interpreted in the stable module category of a finite p-group G, is the statement that a map between finite-dimensional kG-modules factors through a projective if the induced map on Tate cohomology is trivial. We show that Freyd's generating hypothesis holds for a non-trivial finite p-group G if and only if G is either C 2 or(More)
A ghost in the stable module category of a group G is a map between representations of G that is invisible to Tate cohomology. We show that the only non-trivial finite p-groups whose stable module categories have no non-trivial ghosts are the cyclic groups C 2 and C 3. We compare this to the situation in the derived category of a commutative ring. We also(More)
A ghost over a finite p-group G is a map between modular representations of G which is invisible in Tate cohomology. Motivated by the failure of the generating hypothesis—the statement that ghosts between finite-dimensional G-representations factor through a projective—we define the ghost number of kG to be the smallest integer l such that the composite of(More)
For prime power q = p d and a field F containing a root of unity of order q we show that the Galois cohomology ring H * (G F , Z/q) is determined by a quotient G [3] F of the absolute Galois group G F related to its descending q-central sequence. Conversely, we show that G [3] F is determined by the lower cohomology of G F. This is used to give new examples(More)
Let G be a finite group and let k be a field of characteristic p. Given a finitely generated indecomposable non-projective kG-module M , we conjecture that if the Tate cohomologyˆH * (G, M) of G with coefficients in M is finitely generated over the Tate cohomology ringˆH * (G, k), then the support variety V G (M) of M is equal to the entire maximal ideal(More)
We use a K-theory recipe of Thomason to obtain classifications of triangulated subcategories via refining some standard thick subcategory theorems. We apply this recipe to the full subcategories of finite objects in the derived categories of rings and the stable homotopy category of spectra. This gives, in the derived categories, a complete classification(More)