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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)

- SUNIL K. CHEBOLU
- 2012

It is well known that the order statistics of a random sample from the uniform distribution on the interval [0, 1] have Beta distributions. In this paper we consider the order statistics of a random sample of n data points chosen from an arbitrary probability distribution on the interval [0, 1]. For integers k and with 1 ≤ k < ≤ n we find an attainable… (More)

- SUNIL K. CHEBOLU
- 2008

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)

- SUNIL K. CHEBOLU
- 2006

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)

- SUNIL K. CHEBOLU
- 2009

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)

- SUNIL K. CHEBOLU
- 2007

Let G be a finite group and let k be a field whose characteristic p divides the order of G. Freyd's generating hypothesis for the stable module category of G is the statement that a map between finite-dimensional kG-modules in the thick subcategory generated by k factors through a projective if the induced map on Tate cohomology is trivial. We show that if… (More)

Freyd's generating hypothesis for the stable module category of a non-trivial finite group G is the statement that a map between finitely generated kG-modules that belongs to the thick subcategory generated by k factors through a projective if the induced map on Tate cohomology is trivial. In this paper we show that Freyd's generating hypothesis fails for… (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)

- SUNIL K. CHEBOLU
- 2009

In this paper we concentrate on the relations between the structure of small Galois groups, arithmetic of fields, Bloch-Kato conjecture, and Galois groups of maximal prop quotients of absolute Galois groups.

- SUNIL K. CHEBOLU
- 2005

Following Krause [Kra99], we prove Krull-Schmidt theorems for thick subcategories of various triangulated categories: derived categories of rings, noetherian stable homotopy categories, stable module categories over Hopf algebras, and the stable homotopy category of spectra. In all these categories , it is shown that the thick ideals of small objects… (More)