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SFB TRR 358 - Gradu­ate Sem­in­ar Pader­born: Ab­hijit Aryampilly Jay­anthan, "Étale and profin­ite-étale vec­tor bundles on el­lipt­ic curves"

Ort: D 2.314
Veranstalter: Abhijit Aryampilly Jayanthan, Stepan Maximov

Over an algebraically closed field, vector bundles on elliptic curves were classified by Atiyah in 1957. He showed that for a chosen rank and degree, the indecomposable vector bundles are in one to one correspondence with the closed points of the elliptic curve. Further, every vector bundle can be written as a direct sum of its indecomposable subbundles, completing this classification.
The universal profinite-étale cover of an elliptic curve (over some p-adically complete algebraically closed field) is represented by an perfectoid space. With the help of Atiyah's classification, along with some results by Ben Heuer, one is able to classify the collection of all étale (equivalently Zariski) vector bundles which become trivial on some profinite-étale cover of the elliptic curve.


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