##### Department of Mathematics,

University of California San Diego

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### Math 211A - Algebra Seminar

## Eoin Mackall

#### UC San Diego

## Splitting Severi--Brauer varieties by torsors for genus one curves

##### Abstract:

We'll be talking about recent results on the problem of splitting Brauer classes by torsors for genus one curves. In its geometric form the question to be asked is: does every Severi--Brauer variety contain a smooth and projective genus one curve? Algebraically, this question is related to the existence of certain finite Galois modules inside the linear algebraic automorphism group of the Severi--Brauer variety. Our goal will be to motivate why this is an intuitive and interesting question, giving some new results along the way.

### November 27, 2023

### 3:00 PM

APM 7321

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