A Minkowski-style bound for the order of the finite subgroups of the Cremona group of rank 2 over an arbitrary field
By Jean-Pierre Serre. 2009
97 citations recorded by the source corpus.
Let Cr(k) be the Cremona group of rank 2 over a field k, i.e. the group of all k-automorphisms of k(X,Y). We determine the l.c.m. of the orders of the finite subgroups of Cr(k) of order prime to the characteristic of k.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/22b317f92d48224e44410dea37af1bd8ccba1b2e
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In Algebra and Number Theory
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Citations in the corpus
- ON THE MAKAR-LIMANOV, DERKSEN INVARIANTS, AND FINITE AUTOMORPHISM GROUPS OF ALGEBRAIC VARIETIES (2010, background): “If X is rational, then Bir(X) is the Cremona group of rank 2 over k, hence Jordan by [ Se1 , Theorem 5.3], [Se2, Th´eor`eme 3.1].”
- Jordan property for Cremona groups (2012, unknown): “(J.-P. Serre [29, 6.1]) Is the group Cr n ( k ) Jordan?”