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Title:
Bijective Cremona transformations of the plane
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Abstract:
I will discuss birational self-maps of the projective plane over finite fields that induce permutations on the set of rational points. As a main result, we proved that no odd permutation arises over a non-prime finite field of characteristic two, which completes the investigation initiated by Cantat about which permutations can be realized this way. Main ingredients in our proof include the invariance of parity under groupoid conjugations by birational maps, and a list of generators for the group of such maps. This is joint work with Shamil Asgarli, Kuan-Wen Lai, and Susanna Zimmermann.
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