How to use finite fields for problems concerning infinite fields

By Jean-Pierre Serre. 2009

55 citations recorded by the source corpus.

The first part is expository: it explains how finite fields may be used to prove theorems on infinite fields by a reduction mod p process. The second part gives a variant of P.Smith's fixed point theorem which applies in any characteristic.

Subfields: Artificial Intelligence, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/9bda3c8701b4d2eae0a4ade9f49e7ec4103290be

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In Artificial Intelligence

1. L. Illusie
2. Weizhe Zheng
3. V. Popov

In Computational Theory and Mathematics

1. L. Illusie
2. Weizhe Zheng
3. V. Popov

In Geometry and Topology

1. Weizhe Zheng
2. L. Illusie
3. V. Popov

Citations in the corpus

• Odds and Ends on Finite Group Actions and Traces (2010, background): “Recent work of Serre ([Ser07], [Ser09], [Ser10]) has revived interest in them.”
• ON THE MAKAR-LIMANOV, DERKSEN INVARIANTS, AND FINITE AUTOMORPHISM GROUPS OF ALGEBRAIC VARIETIES (2010, background): “Proof. This follows from Theorem 2.22 since in this case (An)G 6= ∅, see [ Se3 , Theorem”