Spectral Sequences
Published:
Basic theory of Spectral Sequences with an application to the Serre-Hochschild Spectral Sequence.
Download here: https://alejandrodlpc.github.io/files/spectral-sequences.pdf
Resources
Disclaimer: These monographs are not peer-reviewed and may contain errors. Some may have incomplete sections as well. Any corrections are welcome!
Hensel’s Lemma
Published:
Basic theory of complete noetherian rings and Hensel’s Lemma.
Download here: https://alejandrodlpc.github.io/files/hensels_lemma.pdf
Etale Algebras
Published:
Basic theory of etale algebras.
Download here: https://alejandrodlpc.github.io/files/etale-algebras.pdf
The Chebotarev Density Theorem and Applications to Computing Galois Groups
Published:
We describe a method of computing Galois groups of polynomials using Frobenius elements.
Download here: https://alejandrodlpc.github.io/files/computing-galois-groups-using-chebotarev-density-theorem.pdf
The Cohomology of Finite Cyclic Groups
Published:
Computation of the group cohomology of finite cyclic groups.
Download here: https://alejandrodlpc.github.io/files/cohomology-of-finite-cyclic-groups.pdf
The Brauer Group of Schemes
Published:
Basic theory of Azumaya Algebras.
Download here: https://alejandrodlpc.github.io/files/brauer-group-of-schemes.pdf
SAGE Code for Hecke Nilpotency
Published:
SAGE code to compute the degree of Hecke nilpotency of level 1 cusp forms modulo 2.
Download here: https://alejandrodlpc.github.io/files/hecke-nilpotency.ipynb