**Date & Time:** Monday, October 07, 2013, 16:00-17:30.

**Venue:** Ramanujan Hall

**Title:** Local Cohomology Modules V

**Speaker: ** Jugal Verma, IIT Bombay

**Abstract:** In this lecture, we will prove Hartshorne-Lichtenbaum Vanishing
Theorem: Let I be an ideal of positive dimension in a complete local domain R
of dimension d. Then the d-th local cohomology module of any R-module M with
support in the closed set V(I) vanishes.

We will see that this plays a crucial role in the proof of Faltings Connectedness Theorem for certain punctured spectra.