Notes and Preprints

My private study note. (Updated January 28, 2024)

All chapters are incomplete. The contents are as follows.

• Chapter 1   On the notion of schemes of graded rings   (Source; Demazure-Gabriel "Introduction to Algebraic Geometry and Algebraic Groups", Chapter 1 )
• Chapter 2   Grothendiek Topos   (Sources; "SGA4", EXPOSE II, III, IV and MacLane-Moerdijk "Sheaves in Geometry and Logic")
• Chapter 3  Elementary Topos   (Source; Johnstone "Topos Theory", Chapter 1 )
• Chapter 4  Topologies and sheaves   (Source; Johnstone "Topos Theory", Chapter 3 )
• Chapter 5  Internal Categories   (Source; Johnstone "Topos Theory", Chapter 2 )
• Chapter 6  Galois category   (Source; "SGA1", EXPOSE V)
• Chapter 7  Model categories for the working mathematicians   (Source; Quillen "Homotopical Algebra", M. Hovey "Model Categories")
• Chapter 8  Study on fibered categories  
• 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.)

1. Complex cobordism theory and groupoid of formal groups (Updated March 7, 2007)
2. Bar spectral sequence (Updated Septmber 1, 2004)
3. Model categories for the working mathematicians March 15-16, 2010 [Keynote file] (Updated March 20, 2015)
4. Toward a representation theory of the group scheme represented by the dual Steenrod algebra March 19, 2015 [Keynote file] (Updated March 20, 2015)
5. Representations of the group represented by the dual Steenrod algebra November 12, 2016 [Keynote file] (Updated November 29,2021)
6. A Convenient Fibered Category for Representation Theory July 12, 2017 [Keynote file] (Updated July 28, 2017)
7. Cohomology Theory and Representation Theory January 25, 2018 [Keynote file] (Updated May 16, 2019)
8. Representation Theory of Hopf Algebroids September 20, 2018 [Keynote file] (Updated October 4, 2018)
9. Representations of Hopf algebras as group actions June 28, 2019 [Keynote file] (Updated July 1, 2019)
10. The Steenrod Algebra from the Group Theoretical Viewpoint October 27, 2019 [Keynote file] (Updated November 29,2021)
11. Representation theory of internal categories and its application to comodules over Hopf algebroids November 9, 2019 [Keynote file] (Updated November 29,2021)
12. On the fibered category of smooth maps and actions of diffeological groupoids Nobember 7, 2020 [Keynote file] (Updated November 29,2021)
13. Unstable modules as representations of Steenrod groups February 17, 2023 (Updated September 11,2023)
14. Representations of groupoids and generalized homology theory October 6, 2023 [Keynote file] (Updated January 28, 2024)
15. A theory of plots January 30, 2024 [Keynote file] (Updated March 19, 2024)
16. Representations of groupoids in the category of plots March 5, 2024 [Keynote file] (Updated March 19, 2024)

1. On excess filtration on the Steenrod algebra Local copy (Updated November 29,2021) Link to Geometry & Topology site
   
2. The Steenrod algebra from the group theoretical viewpoint
   

1. Representations of the Steenrod group (Updated Septmber 11, 2023)
2. Notes on representation theory of internal categories (Updated March 19, 2024)
3. A theory of plots (Updated March 19, 2024)