#### Chandrasekhar Hall

#### Local Cohomology and Completion

#### Rishi Vyas

##### Ben Gurion University, Israel

*Fix an ideal in a commutative noetherian ring. There is an interesting*

relationship between the Local Cohomology and Completion functors at this

ideal: their (right and left, respectively) derived functors are adjoint to

each other, and this adjunction induces an interesting equivalence of

categories. This relationship has been independently studied by a number of

mathematicians over the last few decades: protagonists for this story

include Grothendieck, Matlis, Greenlees-May, Alonso-Jeremias-Lipman,

Schenzel, Porta-Shaul-Yekutieli, and Positselski.

In this expository talk, we will try and describe this relationship by

focusing on the simplest example: an ideal generated by a single element.

The only prerequisites required are a basic understanding of commutative

algebra, and some, again basic, familiarity with chain complexes of modules

over a commutative ring. In particular, most of this talk will not assume

any familiarity with the derived category of a ring.

Done