36 citations · 109 across the 20 of their papers we have counts for
23 papers
Compatibility of -isocrystals on adjoint Shimura varieties
Jake Huryn, Kiran S. Kedlaya, Christian Klevdal +1
In this article, we extend past results of the last two authors to include compatibility of canonical -adic local systems and canonical -isocrystals on adjoint Shimura var…
Compatibility of canonical -adic local systems on Shimura varieties, II
Stefan Patrikis
Let be a Shimura datum. In previous work with Christian Klevdal, we showed that the canonical -valued local systems on Shimura varieties for form…
Compatibility of canonical -adic local systems on Shimura varieties
Christian Klevdal, Stefan Patrikis
For a Shimura variety in the superrigid regime and neat level subgroup , we show that the canonical family of -adic representations associated to a number field…
Trianguline lifts of global mod Galois representations
Najmuddin Fakhruddin, Chandrashekhar Khare, Stefan Patrikis
We show that under a suitable oddness condition, irreducible mod representations of the absolute Galois group of an arbitrary number field have characteristic zero lifts which…
G-rigid local systems are integral
Christian Klevdal, Stefan Patrikis
Let be a reductive group, and let be a smooth quasi-projective complex variety. We prove that any -irreducible, -cohomologically rigid local system on with finite…
Lifting and automorphy of reducible mod p Galois representations over global fields
Najmuddin Fakhruddin, Chandrashekhar Khare, Stefan Patrikis
We extend the lifting methods of our previous paper to lift reducible odd representations of Galois groups of global fields valued…
Potential automorphy of -valued Galois representations
Stefan Patrikis, Shiang Tang
We prove a potentially automorphy theorem for suitable Galois representations and $Γ_{F^+} \to \mathrm{GSpin}_{2n+1}(\o…
Lifting -irreducible but -reducible Galois representations
Najmuddin Fakhruddin, Chandrashekhar Khare, Stefan Patrikis
In recent work, the authors proved a general result on lifting -irreducible odd Galois representations , with $…
Relative deformation theory, relative Selmer groups, and lifting irreducible Galois representations
Najmuddin Fakhruddin, Chandrashekhar Khare, Stefan Patrikis
We study irreducible odd mod Galois representations , for a totally real number field and a ge…
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…
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…
G-Valued Galois Deformation Rings when
Jeremy Booher, Stefan Patrikis
For a smooth group scheme over an extension of such that the generic fiber of is reductive, we study the generic fiber of the Galois deformation ring for a $…
Residual irreducibility of compatible systems
Stefan Patrikis, Andrew Snowden, Andrew Wiles
We show that if is a compatible system of absolutely irreducible Galois representations of a number field then the residual representation is abs…
Deformations of Galois representations and exceptional monodromy, II: raising the level
Stefan Patrikis
Building on lifting results of Ramakrishna, Khare and Ramakrishna proved a purely Galois-theoretic level-raising theorem for two-dimensional odd representations of the Galois group…
Generalized Kuga-Satake theory and good reduction properties of Galois representations
Stefan Patrikis
In previous work we described when a single geometric representation, valued in a linear algebraic group, of the Galois group of a number field lifts through a central torus quotie…
Deformations of Galois representations and exceptional monodromy
Stefan Patrikis
For any simple algebraic group of exceptional type, we construct geometric -adic Galois representations with algebraic monodromy group equal to , in particular produci…
Anabelian geometry and descent obstructions on moduli spaces
Stefan Patrikis, José Felipe Voloch, Yuri Zarhin
We study the section conjecture of anabelian geometry and the sufficiency of the finite descent obstruction to the Hasse principle for the moduli spaces of principally polarized ab…
Generalized Kuga-Satake theory and rigid local systems, I: the middle convolution
Stefan Patrikis
This note explains an approach to producing examples of 'generalized Kuga-Satake theory' based on establishing special cases of Simpson's conjecture that rigid local systems are mo…
Generalized Kuga-Satake theory and rigid local systems, II: rigid Hecke eigensheaves
Stefan Patrikis
This paper uses rigid Hecke eigensheaves, building on Yun's work on the construction of motives with exceptional Galois groups, to produce the first robust examples of `generalized…
Automorphy and irreducibility of some l-adic representations
Stefan Patrikis, Richard Taylor
In this paper we prove that a pure, regular, totally odd, polarizable weakly compatible system of -adic representations is potentially automorphic. The innovation is that we mak…
On the sign of regular algebraic polarizable automorphic representations
Stefan Patrikis
We remove a parity condition from the construction of automorphic Galois representations carried out in the Paris Book Project. We subsequently generalize this construction to the…
Mumford-Tate groups of polarizable Hodge structures
Stefan Patrikis
We classify the possible Mumford-Tate groups of polarizable rational Hodge structures. Along the way we deduce a polarized Hodge-theoretic analogue of a conjectural property of mot…
Variations on a theorem of Tate
Stefan Patrikis
Let be a number field. These notes explore Galois-theoretic, automorphic, and motivic analogues and refinements of Tate's basic result that continuous projective representation…