**Vaibhav Vaish**

TIFR

September 13, 2012

**Weightless Cohomology of Algebraic Varieties**:
We construct a new functorial cohomology theory on the category of varieties over a base field k using mixed hodge modules of Saito (if k is complex numbers) or Frobenius weights (if k is finite). The construction is motivic and naturally arises in the context of Shimura Varieties where it captures the cohomology of Reductive Borel Serre compactification.