##### Department of Mathematics,

University of California San Diego

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### Algebra Seminar

## Manny Reyes

#### UCSD

## On extensions of the functor Spec to noncommutative rings

##### Abstract:

\indent In this talk we will prove the following obstruction result to functors extending the Zariski spectrum: every contravariant functor from rings to sets whose restriction to the full subcategory of commutative rings is isomorphic to Spec must assign the empty set to complex matrix algebras of order at least 3. The proof relies crucially on the Kochen-Specker "no-hidden-variables" theorem of quantum mechanics. We will also discuss a (very) recent generalization of the result due to van den Berg and Heunen.

### February 7, 2011

### 2:00 PM

### AP&M 7321

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