Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Keyword
-
- Absolute Galois group (1)
- Abstract Witt ring (1)
- Algebraic geometry (1)
- Algebras (1)
- Bloch-Kato Conjecture (1)
-
- Elementary Type Conjecture (1)
- Elementary Type pro-$p$-groups (1)
- Finite groups (1)
- Grothendieck filtration (1)
- Hermitian forms (1)
- Koszulity (1)
- Lambda-rings (1)
- Mackey functors (1)
- Positselski's Conjecture (1)
- Pro-$p$-group (1)
- Quadratic forms (1)
- Rings (1)
- Tambara functors (1)
- Universal Koszulity (1)
- Virtual characters (1)
Articles 1 - 3 of 3
Full-Text Articles in Physical Sciences and Mathematics
Albert Forms, Quaternions, Schubert Varieties & Embeddability, Jasmin Omanovic
Albert Forms, Quaternions, Schubert Varieties & Embeddability, Jasmin Omanovic
Electronic Thesis and Dissertation Repository
The origin of embedding problems can be understood as an effort to find some minimal datum which describes certain algebraic or geometric objects. In the algebraic theory of quadratic forms, Pfister forms are studied for a litany of powerful properties and representations which make them particularly interesting to study in terms of embeddability. A generalization of these properties is captured by the study of central simple algebras carrying involutions, where we may characterize the involution by the existence of particular elements in the algebra. Extending this idea even further, embeddings are just flags in the Grassmannian, meaning that their study …
Graded Character Rings, Mackey Functors And Tambara Functors, Beatrice Isabelle Chetard
Graded Character Rings, Mackey Functors And Tambara Functors, Beatrice Isabelle Chetard
Electronic Thesis and Dissertation Repository
Let $G$ be a finite group. The ring $R_\KK(G)$ of virtual characters of $G$ over the field $\KK$ is a $\lambda$-ring; as such, it is equipped with the so-called $\Gamma$-filtration, first defined by Grothendieck. In the first half of this thesis, we explore the properties of the associated graded ring $R^*_\KK(G)$, and present a set of tools to compute it through detailed examples. In particular, we use the functoriality of $R^*_\KK(-)$, and the topological properties of the $\Gamma$-filtration, to explicitly determine the graded character ring over the complex numbers of every group of order at most $8$, as well as …
Enhanced Koszulity In Galois Cohomology, Marina Palaisti
Enhanced Koszulity In Galois Cohomology, Marina Palaisti
Electronic Thesis and Dissertation Repository
Despite their central role in Galois theory, absolute Galois groups remain rather mysterious; and one of the main problems of modern Galois theory is to characterize which profinite groups are realizable as absolute Galois groups over a prescribed field. Obtaining detailed knowledge of Galois cohomology is an important step to answering this problem. In our work we study various forms of enhanced Koszulity for quadratic algebras. Each has its own importance, but the common ground is that they all imply Koszulity. Applying this to Galois cohomology, we prove that, in all known cases of finitely generated pro-$p$-groups, Galois cohomology is …