Conference abstracts

Session S01 - Computational Algebra and Applications of Algebra

July 28, 16:00 ~ 16:25

## Resultants modulo p

### Carlos D'Andrea

### Universitat de Barcelona, Spain - cdandrea@ub.edu

Several problems in elimination theory involving arithmetic over the integers (like resultants, the Nullstellensatz, etc) have as an outcome an integer number which if it is not zero modulo a prime p, often imply that classical results over the complex number (dimension, number of zeroes, etc.) "descend" to the residual field. But what happens when p does divide this number? In this talk, we will show that in the case of multivariate resultants, if the input system has a finite number of zeroes modulo p, then p powered to this cardinality (counted with multiplicities) divides the resultant.

Joint work with Martin Sombra (ICREA & Universitat de Barcelona).