Notes and Preprints
My private study note. (Updated January 28, 2024)
All chapters are incomplete.
The contents are as follows.
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Chapter 1 On the notion of schemes of graded rings
(Source; Demazure-Gabriel "Introduction to Algebraic Geometry and Algebraic Groups", Chapter 1 )
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Chapter 2 Grothendiek Topos (Sources; "SGA4", EXPOSE II,
III, IV and MacLane-Moerdijk "Sheaves in Geometry and Logic")
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Chapter 3 Elementary Topos (Source; Johnstone "Topos Theory", Chapter 1 )
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Chapter 4 Topologies and sheaves (Source; Johnstone "Topos Theory", Chapter 3 )
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Chapter 5 Internal Categories (Source; Johnstone "Topos Theory", Chapter 2 )
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Chapter 6 Galois category (Source; "SGA1", EXPOSE V)
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Chapter 7 Model categories for the working mathematicians
(Source; Quillen "Homotopical Algebra", M. Hovey "Model Categories")
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Chapter 8 Study on fibered categories
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Chapter 9 Representations of internal categories
- Appendix Categories for mathematician reading SGA
(Sources; "SGA4", EXPOSE I, MacLane "Categories for the Working
Mathematician" GTM236, Barr "Exact categories" LNM236, Johnstone
"Adjoint lifting theorems for category of algebras", Bull. Lond. Math.
Soc. 7 (1975), 294-297, etc.)
Lecture notes and slides
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Complex cobordism theory and groupoid of formal groups (Updated March 7, 2007)
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Bar spectral sequence (Updated Septmber 1, 2004)
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Model categories for the working mathematicians March 15-16, 2010
[Keynote file] (Updated March 20, 2015)
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Toward a representation theory of the group scheme represented by the dual Steenrod algebra March 19, 2015
[Keynote file] (Updated March 20, 2015)
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Representations of the group represented by the dual Steenrod algebra November 12, 2016
[Keynote file] (Updated November 29,2021)
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A Convenient Fibered Category for Representation Theory July 12, 2017
[Keynote file] (Updated July 28, 2017)
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Cohomology Theory and Representation Theory January 25, 2018
[Keynote file] (Updated May 16, 2019)
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Representation Theory of Hopf Algebroids September 20, 2018
[Keynote file] (Updated October 4, 2018)
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Representations of Hopf algebras as group actions June 28, 2019
[Keynote file] (Updated July 1, 2019)
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The Steenrod Algebra from the Group Theoretical Viewpoint October 27, 2019
[Keynote file] (Updated November 29,2021)
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Representation theory of internal categories and its application to comodules over Hopf algebroids November 9, 2019
[Keynote file] (Updated November 29,2021)
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On the fibered category of smooth maps and actions of diffeological groupoids November 7, 2020
[Keynote file] (Updated November 29,2021)
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Unstable modules as representations of Steenrod groups February 17, 2023
(Updated September 11,2023)
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Representations of groupoids and generalized homology theory October 6, 2023
[Keynote file] (Updated January 28, 2024)
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A theory of plots January 30, 2024
[Keynote file] (Updated June 29, 2024)
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Representations of groupoids in the category of plots March 5, 2024
[Keynote file] (Updated June 14, 2024)
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A theory of plots June 14, 2024
[Keynote file] (Updated June 29, 2024)
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A theory of plots June 29, 2024
[Keynote file] (Updated June 29, 2024)
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The Steenrod algebra and its representations August 26,27, 2024
[Keynote file]
[PDF file] (Updateted September 26, 2024)
My paper on the Web
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On excess filtration on the Steenrod algebra Local copy (Updated November 29,2021)
Link to Geometry & Topology site
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The Steenrod algebra from the group theoretical viewpoint
Research note---(in progress, highly incomplete)
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Representations of the Steenrod group (Updated Septmber 14, 2024)
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Notes on representation theory of internal categories (Updated August 12, 2024)
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A theory of plots (Updated July 14, 2024)
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