Stefan Patrikis

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20162025

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7 papers · 1 filter

math.NT2025

Compatibility of canonical $ℓ$ -adic local systems on Shimura varieties, II

Stefan Patrikis

Let $(G, X)$ be a Shimura datum. In previous work with Christian Klevdal, we showed that the canonical $G (Q_{ℓ})$ -valued local systems on Shimura varieties for $G$ form…

math.NT2019

Potential automorphy of $GSpin_{2 n + 1}$ -valued Galois representations

Stefan Patrikis, Shiang Tang

We prove a potentially automorphy theorem for suitable Galois representations $Γ_{F^{+}} \to GSpin_{2 n + 1} (F_{p})$ and $Γ_{F^+} \to \mathrm{GSpin}_{2n+1}(\o…

math.NT2019

Lifting $G$ -irreducible but $GL_{n}$ -reducible Galois representations

Najmuddin Fakhruddin, Chandrashekhar Khare, Stefan Patrikis

In recent work, the authors proved a general result on lifting $G$ -irreducible odd Galois representations $Gal (F / F) \to G (F_{ℓ})$ , with $…

math.NT2018

Lifting irreducible Galois representations

Najmuddin Fakhruddin, Chandrashekhar Khare, Stefan Patrikis

We study irreducible mod p representations, valued in general reductive groups, of the Galois group of a number field. When the number field is totally real, we show that odd repre…

math.NT2018

Compatible systems of Galois representations associated to the exceptional group E6

George Boxer, Frank Calegari, Matthew Emerton +3

We construct, over any CM field, compatible systems of l-adic Galois representations that appear in the cohomology of algebraic varieties and have (for all l) algebraic monodromy g…

math.NT2016

Residual irreducibility of compatible systems

Stefan Patrikis, Andrew Snowden, Andrew Wiles

We show that if ${ρ_{ℓ}}$ is a compatible system of absolutely irreducible Galois representations of a number field then the residual representation $ρ_{ℓ}$ is abs…

Compatibility of canonical ℓ-adic local systems on Shimura varieties, II

Potential automorphy of GSpin2n+1​-valued Galois representations