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- 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

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 pro-p-quotients of absolute Galois groups.

Freyd’s generating hypothesis for the stable module category of a nontrivial finite group G is the statement that a map between finitely generated kGmodules 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 kG… (More)

- Sunil K. Chebolu
- 2009

For prime power q = p and a field F containing a root of unity of order q we show that the Galois cohomology ring H∗(GF , Z/q) is determined by a quotient G [3] F of the absolute Galois group GF related to its descending q-central sequence. Conversely, we show that G [3] F is determined by the lower cohomology of GF . This is used to give new examples of… (More)

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 C2 or… (More)

- 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)

- 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 C2 and C3. We compare this to the situation in the derived category of a commutative ring. We also… (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)

- Sunil K. Chebolu
- 2008

We use a K-theory recipe of Thomason to obtain classi cations of triangulated subcategories via re ning some standard thick subcategory theorems. We apply this recipe to the full subcategories of nite objects in the derived categories of rings and the stable homotopy category of spectra. This gives, in the derived categories, a complete classi cation of the… (More)

The smallest non-abelian p-groups play a fundamental role in the theory of Galois p-extensions. We illustrate this by highlighting their role in the definition of the norm residue map in Galois cohomology. We then determine how often these groups — as well as other closely related, larger p-groups — occur as Galois groups over given base fields. We show… (More)