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
Full-text PDF
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.
- [1] 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
- [2] Ivo Dell’Ambrogio and Greg Stevenson, On the derived category of a graded commutative Noetherian ring, J. Algebra 373 (2013), 356–376. MR 2995031, https://doi.org/10.1016/j.jalgebra.2012.09.038
- [3] Mark Hovey, Model categories, Mathematical Surveys and Monographs, vol. 63, American Mathematical Society, Providence, RI, 1999. MR 1650134
- [4] Birger Iversen, Cohomology of sheaves, Universitext, Springer-Verlag, Berlin, 1986. MR 842190
- [5] 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
- [6] Arthur Ogus, On the logarithmic Riemann-Hilbert correspondence, Doc. Math. Extra Vol. (2003), 655–724. Kazuya Kato’s fiftieth birthday. MR 2046612
- [7] Kazuya Kato and Chikara Nakayama, Log Betti cohomology, log étale cohomology, and log de Rham cohomology of log schemes over 𝐶, Kodai Math. J. 22 (1999), no. 2, 161–186. MR 1700591, https://doi.org/10.2996/kmj/1138044041
- [8]
Clemens Koppensteiner,
The de Rham functor for logarithmic d-modules,
arXiv e-prints, 4 2019. - [9] Clemens Koppensteiner and Mattia Talpo, Holonomic and perverse logarithmic D-modules, Adv. Math. 346 (2019), 510–545. MR 3911632, https://doi.org/10.1016/j.aim.2019.02.016
- [10]
The Stacks Project Authors,
Stacks project, http://stacks.math.columbia.edu.
, Kodai Math. J. 22 (1999), no. 2, 161-186. Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 54B40, 18F20, 55M05
Retrieve articles in all journals with MSC (2010): 54B40, 18F20, 55M05
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
Email:
clemens.koppensteiner@maths.ox.ac.uk
DOI:
https://doi.org/10.1090/proc/14867
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
