Personal notes
These are notes written for myself to better understand some papers/books and make comments to them. Use at your own risk.
0) Comments to small FLE (last modified July 16, 2024)
1) Comments to: D. Arinkin, D. Gaitsgory, D. Kazhdan, S. Raskin, N. Rozenblyum, Y. Varshavsky, The stack of local systems with restricted variation and geometric Langlands theory with nilpotent singular support, arxiv version 2, and Duality for automorphic sheaves with nilpotent singular support, arxiv version 2
I try to give detailed explanations and justify certains things which
were not clear to me (and were left to a reader) in the cited papers.
2) Assumptions on the sheaf theory for the small FLE paper. (last modified August 9, 2024)
3) Analog of the theta-sheaf on the 3-fold metaplectic cover of G_2? (last modified 10 Oct 2021)
4) My notes of Embryo GL seminar (organized by D. Gaitsgory) (last modified March 29, 2024)
Notes mostly about commutative factorization algebras.
5) Comments to Gaitsgory, The local and global versions of the Whittaker category (last modified May 7, 2024)
We give detailed explanations of many claims left to a reader in this paper.
6) Comments to D. Gaitsgory, S. Lysenko, Parameters and duality for the metaplectic geometric Langlands theory (last modified: April 7, 2024)
We give some more detailed explanations of some points than those
from the main text. (the latest corrected version of the paper itself is
available here).
7) Comments to Beilinson, Drinfeld, Chiral algebras, Colloquium Publications, vol. 51, 2004 (last modified 12 dec 2017)
We develop to some extent the theory of chiral algebras
for perverse sheaves. For example, we explain the existence of free
chiral algebras and enveloping chiral algebras of Lie-* algebras in the
setting of perverse sheaves.
8) Comments to Rozenblyum, Gaitsgory, A Study in Derived Algebraic Geometry: Volumes I and II, Mathematical Surveys and Monographs
Volume: 221; 2017 (last modified 6 Dec., 2024, 268 pages)
We prove many claims left
for a reader in this book and some others used in practice. The latest corrected version of this book is found on
Dennis Gaitsgory's homepage. Some notions from higher algebra are
introduced and discussed in the model-independent setting, for
example oo-operads, relative undercategory construction, relative
colimit, relative Kan extension, flat morphism of oo-categories. We
also prove some claims of the derived algebraic geomery left to a
reader in this book.
9) Comments to Braverman, Gaitsgory, Deformations of Local Systems and Eisenstein Series, GAFA 2008, Vol. 17, Issue 6, 1788 - 1850 (last modified 18 Dec 2017)
Many things are left for a reader to be worked out himself. We work out some of them.
10) Comments to Feigin,
Finkelberg, Kuznetsov, Mirković, Ivan Semi-infinite flags. II. Local
and global intersection cohomology of quasimaps' spaces. Differential
topology, infinite-dimensional Lie algebras, and applications, 113 - 148,
Amer. Math. Soc. Transl. Ser. 2, 194, Adv. Math. Sci., 44, Amer. Math.
Soc., Providence, RI, 1999 (last modified 23 dec 2017)
We give a new proof of a result of this paper, which allows to
avoid the theory of weights. This simplifies the
definition of the action of the dual Lie algebra on the
Eisenstein series corresponding to the trivial local system.
11) Comments to S. Raskin, Chiral categories (last modified 20 dec 2019)
We justify certain things left to a reader
Weakly multiplicative quasi-coherent sheaves (last modified 23 Nov 2019)
This note contains some examples of these objects introduced in Raskin, Chiral categories
12) Comment to Gaitsgory, Sheaves of categories and notion of 1-affineness (last modified 23 Jan 2024)
We justify certain things left to a reader
13) Comments to Krahmer, Notes on Koszul algebras (last modified 29 Sept 2017)