Arithmetic & Homotopic Galois Theory IRN | Transfer principles for Galois cohomology and Serre's conjecture II

February 4, 2026	Transfer principles for Galois cohomology and Serre's conjecture II Diego Izquierdo, IMJ-PRG Université Paris Cité, France RIMS Kyoto (Room 110) + Zoom · JP: 16:30 · FR: 08:30 In this talk, I will present some transfer principles for the cohomological dimension of fields. I will then show some applications to Serre's Conjecture II, which predicts a characterization of cohomological dimension 2 fields in terms of rational points on torsors under algebraic groups. In particular, we will see that Serre's Conjecture II for characteristic zero fields implies the same conjecture for positive characteristic fields. This is joint work with Giancarlo Lucchini Arteche.
P. Gille. Serre's conjecture II a survey. Quadratic forms, linear algebraic groups, and cohomology, Developments mathematics 18, p. 41-56, Springer, 2010 [preprint] D. Izquierdo, G. Lucchini Arteche. Homogeneous spaces, algebraic K-theory and cohomological dimension of fields, Journal of the European Mathematical Society, Vol. 24(6), p. 2169–2189, 2022. D. Izquierdo, G. Lucchini Arteche. Transfer principles for Galois cohomology and Serre's conjecture II. Advances in Mathematics, vol. 480, Part C, 110532, 2025 [ArXiV]
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February 4, 2026

Transfer principles for Galois cohomology and Serre's conjecture II

Diego Izquierdo, IMJ-PRG Université Paris Cité, France RIMS Kyoto (Room 110) + Zoom · JP: 16:30 · FR: 08:30

In this talk, I will present some transfer principles for the cohomological dimension of fields. I will then show some applications to Serre's Conjecture II, which predicts a characterization of cohomological dimension 2 fields in terms of rational points on torsors under algebraic groups. In particular, we will see that Serre's Conjecture II for characteristic zero fields implies the same conjecture for positive characteristic fields. This is joint work with Giancarlo Lucchini Arteche.

P. Gille. Serre's conjecture II a survey. Quadratic forms, linear algebraic groups, and cohomology, Developments mathematics 18, p. 41-56, Springer, 2010 [preprint]
D. Izquierdo, G. Lucchini Arteche. Homogeneous spaces, algebraic K-theory and cohomological dimension of fields, Journal of the European Mathematical Society, Vol. 24(6), p. 2169–2189, 2022.
D. Izquierdo, G. Lucchini Arteche. Transfer principles for Galois cohomology and Serre's conjecture II. Advances in Mathematics, vol. 480, Part C, 110532, 2025 [ArXiV]