Advanced search options

Sorted by: relevance · author · university · date | New search

You searched for `subject:( coboundaries)`

.
Showing records 1 – 2 of
2 total matches.

▼ Search Limiters

Boston College

1. Harvey, Ebony Ann. Cohomological Invariants of Quadratic Forms.

Degree: MA, Mathematics, 2010, Boston College

URL: http://dlib.bc.edu/islandora/object/bc-ir:101504

Given a field F, an
algebraic closure K and an
F-vector space
V, we can tensor the space
V with the algebraic closure
K. Two quadratic spaces of the same
dimension become isomorphic when tensored with an algebraic
closure. The failure of this isomorphism over
F is measured by the Hasse invariant.
This paper explains how the determinants and Hasse Invariants of
quadratic forms are related to certain cohomology classes
constructed from specific short exact sequences. In particular, the
Hasse Invariant is defined as an element of the Brauer
group.
*Advisors/Committee Members: Benjamin V. Howard (Thesis advisor).*

Subjects/Keywords: Central Simple Algebra; cocycles and coboundaries; Cohomology; factor sets; Hasse Invariant; Quadratic Forms

Record Details Similar Records

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Harvey, E. A. (2010). Cohomological Invariants of Quadratic Forms. (Masters Thesis). Boston College. Retrieved from http://dlib.bc.edu/islandora/object/bc-ir:101504

Chicago Manual of Style (16^{th} Edition):

Harvey, Ebony Ann. “Cohomological Invariants of Quadratic Forms.” 2010. Masters Thesis, Boston College. Accessed December 16, 2019. http://dlib.bc.edu/islandora/object/bc-ir:101504.

MLA Handbook (7^{th} Edition):

Harvey, Ebony Ann. “Cohomological Invariants of Quadratic Forms.” 2010. Web. 16 Dec 2019.

Vancouver:

Harvey EA. Cohomological Invariants of Quadratic Forms. [Internet] [Masters thesis]. Boston College; 2010. [cited 2019 Dec 16]. Available from: http://dlib.bc.edu/islandora/object/bc-ir:101504.

Council of Science Editors:

Harvey EA. Cohomological Invariants of Quadratic Forms. [Masters Thesis]. Boston College; 2010. Available from: http://dlib.bc.edu/islandora/object/bc-ir:101504

Universitetet i Tromsø

2. Breivik, Markus Nordvoll. Group Cohomology and Extensions .

Degree: 2019, Universitetet i Tromsø

URL: http://hdl.handle.net/10037/16251

The goal of this thesis is to classify all extensions where the kernel has order p^s and the cokernel has order p^t, p is a prime, and 1 ≤ s,t ≤ 2. We determine (up to weak congruence) the different combinations of kernel, cokernel and operators, and for each case, calculate the second cohomology group. By comparing resolutions, we get an explicit correspondence between the second cohomology group and the group of congruence classes of extensions. Using this construction, we determine (up to congruence) the extensions for the different combinations.
*Advisors/Committee Members: Prasolov, Andrei (advisor).*

Subjects/Keywords: VDP::Mathematics and natural science: 400::Mathematics: 410::Algebra/algebraic analysis: 414; VDP::Matematikk og Naturvitenskap: 400::Matematikk: 410::Algebra/algebraisk analyse: 414; homological algebra; homology; cohomology; group cohomology; group extension; group extensions; integral group ring; short exact sequence; exact sequence; resolution; module; modules; p-groups; cocycle; cocycles; coboundary; coboundaries; resolutions; kernel; cokernel

Record Details Similar Records

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Breivik, M. N. (2019). Group Cohomology and Extensions . (Masters Thesis). Universitetet i Tromsø. Retrieved from http://hdl.handle.net/10037/16251

Chicago Manual of Style (16^{th} Edition):

Breivik, Markus Nordvoll. “Group Cohomology and Extensions .” 2019. Masters Thesis, Universitetet i Tromsø. Accessed December 16, 2019. http://hdl.handle.net/10037/16251.

MLA Handbook (7^{th} Edition):

Breivik, Markus Nordvoll. “Group Cohomology and Extensions .” 2019. Web. 16 Dec 2019.

Vancouver:

Breivik MN. Group Cohomology and Extensions . [Internet] [Masters thesis]. Universitetet i Tromsø 2019. [cited 2019 Dec 16]. Available from: http://hdl.handle.net/10037/16251.

Council of Science Editors:

Breivik MN. Group Cohomology and Extensions . [Masters Thesis]. Universitetet i Tromsø 2019. Available from: http://hdl.handle.net/10037/16251