Reciprocity laws for representations of finite groups (2009)
Chebolu, Sunil K., Minac, Jan, Reis, Clive
Much has been written on reciprocity laws in number theory and their connections with group representations. In this paper we explore more on these connections. We prove a "reciprocity Law" for...
Hamlet and Pfister forms (A tragedy in four acts) (2009)
In the mid-1960s A. Pfister discovered extraordinary, strongly multiplicative forms which are now called Pfister forms. From that time on, these forms played a dominant role in the theory of...
Galois module structure of Galois cohomology for embeddable cyclic extensions of degree p^n (2009)
Lemire, Nicole, Minac, Jan, Schultz, Andrew, Swallow, John
Let p>2 be prime, and let n,m be positive integers. For cyclic field extensions E/F of degree p^n that contain a primitive pth root of unity, we show that the associated F_p[Gal(E/F)]-modules...
Mild pro-2-groups and 2-extensions of Q with restricted ramification (2009)
Using the mixed Lie algebras of Lazard, we extend the results of the first author on mild groups to the case p=2. In particular, we show that for any finite set S_0 of odd rational primes we can find...
On the descending central sequence of absolute Galois groups (2008)
Let $p$ be an odd prime number and $F$ a field containing a primitive $p$th root of unity. We prove a new restriction on the group-theoretic structure of the absolute Galois group $G_F$ of $F$....
Freyd's generating hypothesis with almost split sequences (2008)
Carlson, Jon F., Chebolu, Sunil K., Minac, Jan
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...
Finite generation of Tate cohomology (2008)
Carlson, Jon F., Chebolu, Sunil K., Minac, Jan
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 cohomology $\HHHH^*(G, M)$ of G...
GALOIS MODULE STRUCTURE OF pTH-POWER Classes Of Extensions Of Degree p (2007)
For fields F of characteristic not p containing a primitive pth root of unity, we determine the Galois module structure of the group of pth-power classes of K for all cyclic extensions K/F of degree...
The generating hypothesis for the stable module category of a $p$-group (2006)
Benson, David J., Chebolu, Sunil K., Christensen, J. Daniel, Minac, Jan
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...
Detecting pro-p-groups that are not absolute Galois groups (2006)
Benson, Dave, Lemire, Nicole, Minac, Jan, Swallow, John
We present several constraints on the absolute Galois groups G_F of fields F containing a primitive pth root of unity, using restrictions on the cohomology of index p normal subgroups from a previous...
Detecting pro-p-groups that are not absolute Galois groups, expanded version (2006)
Benson, Dave, Lemire, Nicole, Minac, Jan, Swallow, John
We present several constraints on the absolute Galois groups G_F of fields F containing a primitive pth root of unity, using restrictions on the cohomology of index p normal subgroups from a previous...
Groups which do not admit ghosts (2006)
Chebolu, Sunil K., Christensen, J. Daniel, Minac, Jan
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...
Ghosts in modular representation theory (2006)
Chebolu, Sunil K., Christensen, J. Daniel, Minac, Jan
Let $G$ be a finite $p$-group and let $k$ be a field of characteristic $p$. Recall that the \emph{stable module category} $\StMod(kG)$ is the following tensor triangulated category. The objects are...
Automatic realizations of Galois groups with cyclic quotient of order p^n (2006)
Minac, Jan, Schultz, Andrew, Swallow, John
We establish automatic realizations of Galois groups among groups M\rtimes G, where G is a cyclic group of order p^n for a prime p and M is a quotient of the group ring Fp[G].
Galois module structure of Milnor K-theory mod p^s in characteristic p (2006)
Minac, Jan, Schultz, Andrew, Swallow, John
Let E be a cyclic extension of pth-power degree of a field F of characteristic p. For all m, s in N, we determine K_mE/p^sK_mE as a (Z/p^sZ)[Gal(E/F)]-module. We also provide examples of extensions...
Hilbert 90 for Galois cohomology (2006)
Lemire, Nicole, Minac, Jan, Schultz, Andrew, Swallow, John
Assuming the Bloch-Kato Conjecture, we determine precise conditions under which Hilbert 90 is valid for Milnor k-theory and Galois cohomology. In particular, Hilbert 90 holds for degree n when the...
Hilbert 90 for biquadratic extensions (2005)
Dwilewicz, Roman, Minac, Jan, Schultz, Andrew, Swallow, John
Hilbert's Theorem 90 is a classical result in the theory of cyclic extensions. The quadratic case of Hilbert 90, however, generalizes in noncyclic directions as well. Informed by a poem of Richard...
Demuskin groups, Galois modules, and the elementary type conjecture (2005)
Labute, John, Lemire, Nicole, Minac, Jan, Swallow, John
Let p be a prime and F(p) the maximal p-extension of a field F containing a primitive p-th root of unity. We give a new characterization of Demuskin groups among Galois groups Gal(F(p)/F) when p=2,...
Cohomological dimension and Schreier's formula in Galois cohomology (2004)
Labute, John, Lemire, Nicole, Minac, Jan, Swallow, John
Let p be a prime and F a field containing a primitive pth root of unity. Then for n in N, the cohomological dimension of the maximal pro-p-quotient G of the absolute Galois group of F is H^n(G,Fp)...
When is Galois cohomology free or trivial? (2004)
Lemire, Nicole, Minac, Jan, Swallow, John
Let p be a prime and F a field containing a primitive pth root of unity. Let E/F be a cyclic extension of degree p and G_E < G_F the associated absolute Galois groups. We determine precise conditions...
Cyclic algebras and construction of some Galois modules (2004)
Minac, Jan, Schultz, Andrew, Swallow, John
Let p be a prime and suppose that K/F is a cyclic extension of degree p^n with group G. Let J be the F_pG-module K^*/K^{*p} of pth-power classes. In our previous paper we established precise...
Galois module structure of pth-power classes of cyclic extensions of degree p^n (2004)
Minac, Jan, Schultz, Andrew, Swallow, John
In the mid-1960s Borevic and Faddeev initiated the study of the Galois module structure of groups of pth-power classes of cyclic extensions K/F of pth-power degree. They determined the structure of...
Galois module structure of Galois cohomology and partial Euler-Poincare characteristics (2004)
Lemire, Nicole, Minac, Jan, Swallow, John
Let F be a field containing a primitive pth root of unity, and let U be an open normal subgroup of index p of the absolute Galois group G_F of F. Using the Bloch-Kato Conjecture we determine the...
Galois module structure of Milnor K-theory in characteristic p (2004)
Bhandari, Ganesh, Lemire, Nicole, Minac, Jan, Swallow, John
Let E be a cyclic extension of degree p^n of a field F of characteristic p. Using arithmetic invariants of E/F we determine k_mE, the Milnor K-groups K_mE modulo p, as Fp[Gal(E/F)]-modules for all m...
Galois embedding problems with cyclic quotient of order p (2003)
Let K/F be a cyclic field extension of odd prime degree. We consider Galois embedding problems involving Galois groups with common quotient Gal(K/F) such that corresponding normal subgroups are...
The first two cohomology groups of some Galois groups (2003)
We investigate the first two Galois cohomology groups of $p$-extensions over a base field which does not necessarily contain a primitive $p$th root of unity. We use twisted coefficients in a...
Construction and classification of some Galois modules (2003)
In our previous paper we describe the Galois module structures of $p$th-power class groups $K^\times/{K^{\times p}}$, where $K/F$ is a cyclic extension of degree $p$ over a field $F$ containing a...
Construction And Classification Of Some Galois Modules (2003)
In our previous paper we describe the Galois module structures of pth-power class groups K /K p , where K/F is a cyclic extension of degree p over a field F containing a primitive pth root of unity....
Galois Groups Over Nonrigid Fields (2000)
Gao, Wenfeng, Leep, David B., Minac, Jan, Smith, Tara L.
Let $F$ be a field with characteristic $\neq 2$. We show that $F$ is a nonrigid field if and only if certain small 2-groups occur as Galois groups over $F$. These results provide new "automatic...
Field theory and the Cohomology of Some Galois Groups (2000)
Adem, Alejandro, Gao, Wenfeng, Karagueuzian, Dikran, Minac, Jan
We prove that two arithmetically significant extensions of a field F coincide if and only if the Witt ring WF is a group ring Z/n[G]. Furthermore, working modulo squares with Galois groups which are...
On the cohomology of Galois groups determined by Witt rings (1998)
Adem, Alejandro, Karagueuzian, Dikran, Minac, Jan
Let F denote a field of characteristic different from two. In this paper we describe the mod 2 cohomology of a Galois group which is determined by the Witt ring WF.
On the Cohomology of Galois Groups Determined by Witt Rings
Alejandro Adem, Dikran B. Karagueuzian, Jan Minac
. Let F denote a field of characteristic different from two. In this paper we describe the mod 2 cohomology of a Galois group GF (called the W-group of F ) which is known to essentially characterize...