Prof. Dr. Annette Huber-Klawitter, Albert-Ludwigs-Universität Freiburg, Vortrag: Differential forms in algebraic geometry -- a new perspective in the singular case
Donnerstag, 19.11.2015 16:30 im Raum M5
Differential forms originally show up when integrating or differentiating
on manifolds. However, the concept also makes perfect sense on algebraic
varieties because the derivative of a polynomial is a polynomial.
The object has very many important uses, e.g., as a source of invariants
needed in order to classify varieties. This approach was very successful
for smooth varieties, but the singular case is less well-understood.
We explain how the use of the h-topology (introduced by Suslin
and Voevodsky in order to study motives) gives a very good object also
in the singular case, at least in characteristic zero. The approach unifies
other ad-hoc notions and simplies many proofs. We also explain the
necessary modifications in positive characteristic and the new problems that