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Orlov spectra as a filtered cohomology theory
Ludmil Katzarkov1, Gabriel Kerr
1Department of Mathematics, University of Miami, Coral Gables, FL, 33146, USA ; Fakultät für Mathematik, Universität Wien, 1090 Wien, Austria.
Advances in Mathematics
|August 24, 2013
Summary
This study introduces a novel dimension theory for triangulated categories. It leverages invariants from the pretriangulated setting for new insights.
Area of Science:
- Algebraic Geometry
- Category Theory
Background:
- Dimension theory is crucial in algebraic geometry.
- Triangulated categories are fundamental in abstract algebra and topology.
Purpose of the Study:
- To develop a new dimension theory for triangulated categories.
- To explore invariants within the pretriangulated setting.
Main Methods:
- Investigating invariants arising from the pretriangulated setting.
- Applying these invariants to dimension theory.
Main Results:
- A new framework for dimension theory in triangulated categories.
- Identification of novel invariants.
Conclusions:
- The pretriangulated setting offers a powerful perspective for dimension theory.
- This approach expands the understanding of triangulated categories.
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