# AIS - Advanced commutative algebra (2019)

## Venue: IIT, Kharagpur

## Dates: 2 Dec 2019 to 14 Dec 2019

Convener(s) |
|||

Name: |
Prof. Mousumi Mandal |
Prof. Ramakrishna Nanduri | Prof Manoj Kummini |

Mailing Address: |
Department of Mathematics |
Department of Mathematics IIT Kharagpur West Bengal-721302 |
Chennai Mathematical Institute |

Email: |
mousumi at maths.iitkgp.ac.in | nanduri at maths.iitkgp.ac.in | mkummini at cmi.ac.in |

This school covers topics in an advanced course in commutative algebra. Topics to be discussed include: flatness, criterion for flatness, fibres of flat maps, generic flatness theorem; Kahler differentials, fundamental exact sequences; completion; smoothness; jacobian criterion; Cohen structure theorem (equicharacteristic case); excellent rings; Lichtenbaum-Schlessinger functors. The prerequisite for this school is a course in introductory commutative algebra (associated primes and primary decomposition; integral extensions; dimension theory of noetherian local rings).