Graded topological spaces
Author:
Clemens Koppensteiner
Journal:
Proc. Amer. Math. Soc. 148 (2020), 1325-1338
MSC (2010):
Primary 54B40, 18F20; Secondary 55M05
DOI:
https://doi.org/10.1090/proc/14867
Published electronically:
December 6, 2019
MathSciNet review:
4055958
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Abstract | References | Similar Articles | Additional Information
Abstract: We introduce the notion of a “graded topological space”: a topological space endowed with a sheaf of abelian groups which we think of as a sheaf of gradings. Any object living on a graded topological space will be graded by this sheaf of abelian groups. We work out the fundamentals of sheaf theory and Poincaré–Verdier duality for such spaces.
- Denis-Charles Cisinski and Frédéric Déglise, Local and stable homological algebra in Grothendieck abelian categories, Homology Homotopy Appl. 11 (2009), no. 1, 219–260. MR 2529161
- Ivo Dell’Ambrogio and Greg Stevenson, On the derived category of a graded commutative Noetherian ring, J. Algebra 373 (2013), 356–376. MR 2995031, DOI https://doi.org/10.1016/j.jalgebra.2012.09.038
- Mark Hovey, Model categories, Mathematical Surveys and Monographs, vol. 63, American Mathematical Society, Providence, RI, 1999. MR 1650134
- Birger Iversen, Cohomology of sheaves, Universitext, Springer-Verlag, Berlin, 1986. MR 842190
- Masaki Kashiwara and Pierre Schapira, Sheaves on manifolds, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 292, Springer-Verlag, Berlin, 1994. With a chapter in French by Christian Houzel; Corrected reprint of the 1990 original. MR 1299726
- Arthur Ogus, On the logarithmic Riemann-Hilbert correspondence, Doc. Math. Extra Vol. (2003), 655–724. Kazuya Kato’s fiftieth birthday. MR 2046612
- Kazuya Kato and Chikara Nakayama, Log Betti cohomology, log étale cohomology, and log de Rham cohomology of log schemes over ${\bf C}$, Kodai Math. J. 22 (1999), no. 2, 161–186. MR 1700591, DOI https://doi.org/10.2996/kmj/1138044041
- Clemens Koppensteiner, The de Rham functor for logarithmic d-modules, arXiv e-prints, 4 2019.
- Clemens Koppensteiner and Mattia Talpo, Holonomic and perverse logarithmic D-modules, Adv. Math. 346 (2019), 510–545. MR 3911632, DOI https://doi.org/10.1016/j.aim.2019.02.016
- The Stacks Project Authors, Stacks project, http://stacks.math.columbia.edu.
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Additional Information
Clemens Koppensteiner
Affiliation:
Institute for Advanced Study, 1 Einstein Drive, Princeton, New Jersey 08540
Address at time of publication:
Mathematical Institute, University of Oxford, Andrew Wiles Building, Oxford, OX2 6GG, United Kingdom
MR Author ID:
1129312
Email:
clemens.koppensteiner@maths.ox.ac.uk
Received by editor(s):
July 1, 2019
Published electronically:
December 6, 2019
Additional Notes:
The author was supported by the National Science Foundation under Grant No. DMS-1638352.
Communicated by:
Alexander Braverman
Article copyright:
© Copyright 2019
American Mathematical Society
