Il 5 e 6 Novembre 2025, per il ciclo “Crossings - Math Seminars”, Alexander Merkurjev (University of California at Los Angeles) terrà i seguenti interventi:
#1
Technical Seminar: Negligible Galois cohomology
Abstract: An important problem in Galois theory is the profinite inverse Galois problem, which asks how to characterize absolute Galois groups of fields among all profinite groups. While an answer to this question is not known, even conjecturally, several necessary conditions for a profinite group to be an absolute Galois group have been established. One of such conditions is given in terms of so-called negligible Galois cohomology introduced by Serre. We will give definitions, examples of negligible cohomology and relate it to cohomological invariants of algebraic groups and to the embedding problem for fields.
Data e ora: Mercoledì 5 Novembre, ore 15:00
Luogo: Edificio U1-08, Piazza della Scienza - Università di Milano-Bicocca
#2
Math Forum: The lifting problem for Galois representations
Abstract: For every finite group H and every finite H-module A, we determine the subgroup of negligible classes in H^2(H, A), in the sense of Serre, over fields with enough roots of unity. Using this, we determine all pairs (n, p), where n is a positive integer and p is a prime number, such that for every field F, every continuous homomorphism Γ_F → GL_n(Z/pZ), where Γ_F is the absolute Galois group of F, lifts to GL_n(Z/p^2Z). This is a joint work with Federico Scavia.
Data e ora: Giovedì 6 Novembre, ore 15:00
Luogo: Edificio U1-08, Piazza della Scienza - Università di Milano-Bicocca
Al termine dei seminari seguirà un aperitivo
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