scholarly journals Scalar extensions of categorical resolutions of singularities

2018 ◽  
Vol 222 (7) ◽  
pp. 1565-1578
Author(s):  
Zhaoting Wei
Keyword(s):  
Scalar Extensions

Quadratic Forms

2017 ◽  
Author(s):  
Bernhard M¨uhlherr ◽  
Holger P. Petersson ◽  
Richard M. Weiss
Keyword(s):  
Quadratic Forms ◽  
Splitting Field ◽  
Quadratic Space ◽  
Polar Spaces ◽  
Quadratic Module ◽  
Quadratic Modules ◽  
Hyperbolic Planes ◽  
Scalar Extensions

This chapter presents a few standard definitions and results about quadratic forms and polar spaces. It begins by defining a quadratic module and a quadratic space and proceeds by discussing a hyperbolic quadratic module and a hyperbolic quadratic space. A quadratic module is hyperbolic if it can be written as the orthogonal sum of finitely many hyperbolic planes. Hyperbolic quadratic modules are strictly non-singular and free of even rank and they remain hyperbolic under arbitrary scalar extensions. A hyperbolic quadratic space is a quadratic space that is hyperbolic as a quadratic module. The chapter also considers a split quadratic space and a round quadratic space, along with the splitting extension and splitting field of of a quadratic space.

scholarly journals Disformal Transformations in Scalar–Torsion Gravity

Universe ◽  
2019 ◽  
Vol 5 (7) ◽  
pp. 167 ◽  
Author(s):  
Manuel Hohmann
Keyword(s):  
Gravitational Interaction ◽  
Teleparallel Gravity ◽  
Generic Class ◽  
Flat Metric ◽  
Scalar Extensions

We study disformal transformations in the context of scalar extensions to teleparallel gravity, in which the gravitational interaction is mediated by the torsion of a flat, metric compatible connection. We find a generic class of scalar–torsion actions which is invariant under disformal transformations, and which possesses different invariant subclasses. For the most simple of these subclasses we explicitly derive all terms that may appear in the action. We propose to study actions from this class as possible teleparallel analogues of healthy beyond Horndeski theories.

scholarly journals Scalar extensions of derived categories and non-Fourier–Mukai functors

2015 ◽  
Vol 281 ◽  
pp. 1100-1144 ◽  
Author(s):  
Alice Rizzardo ◽  
Michel Van den Bergh
Keyword(s):  
Derived Categories ◽  
Scalar Extensions
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