# The p-adic analytic space of pseudocharacters of a profinite group and pseudorepresentations over arbitrary rings

@article{Chenevier2008ThePA, title={The p-adic analytic space of pseudocharacters of a profinite group and pseudorepresentations over arbitrary rings}, author={Ga{\"e}tan Chenevier}, journal={arXiv: Number Theory}, year={2008} }

Let G be a profinite group which is topologically finitely generated, p a prime number and d an integer. We show that the functor from rigid analytic spaces over Q_p to sets, which associates to a rigid space Y the set of continuous d-dimensional pseudocharacters G -> O(Y), is representable by a quasi-Stein rigid analytic space X, and we study its general properties. Our main tool is a theory of "determinants" extending the one of pseudocharacters but which works over an arbitrary base ring; an…

## 109 Citations

### On density of modular points in pseudo-deformation rings

- Mathematics
- 2021

. Given a continuous, odd, reducible and semi-simple 2-dimensional representation ¯ ρ 0 of G Q ,Np over a ﬁnite ﬁeld of odd characteristic p , we study the relation between the universal deformation…

### On the infinite fern of Galois representations of unitary type

- Mathematics
- 2009

Let E be a CM number field, F its maximal totally real subfield, c the generator of Gal(E/F), p an odd prime totally split in E, and S a finite set of places of E containing the places above p.
Let…

### Algebraic families of Galois representations and potentially semi-stable pseudodeformation rings

- Mathematics
- 2015

We construct and study the moduli of continuous representations of a profinite group with integral p-adic coefficients. We present this moduli space over the moduli space of continuous…

### Algebraic families of Galois representations and potentially semi-stable pseudodeformation rings

- MathematicsMathematische Annalen
- 2017

We construct and study the moduli of continuous representations of a profinite group with integral p-adic coefficients. We present this moduli space over the moduli space of continuous…

### Sur la densité des représentations cristallines du groupe de Galois absolu de Q_p

- Mathematics
- 2010

Let X_d be the p-adic analytic space classifying the d-dimensional (semisimple) p-adic Galois representations of the absolute Galois group of Q_p. We show that the crystalline representations are…

### Congruences of algebraic automorphic forms and supercuspidal representations

- MathematicsCambridge Journal of Mathematics
- 2021

Let $G$ be a connected reductive group over a totally real field $F$ which is compact modulo center at archimedean places. We find congruences modulo an arbitrary power of p between the space of…

### Moduli of Galois Representations

- Mathematics
- 2013

The theme of this thesis is the study of moduli stacks of representations of an associative algebra, with an eye toward continuous representations of profinite groups such as Galois groups. The…

### Integrality of the Betti moduli space

- Mathematics
- 2022

. If in a given rank r , there is an irreducible complex local system with torsion determinant and quasi-unipotent monodromies at inﬁnity on a smooth quasi-projective variety, then for every prime…

### Irreducibility of versal deformation rings in the (p,p)-case for 2-dimensional representations

- Mathematics
- 2015

### Images of Pseudo-Representations and Coefficients of Modular Forms modulo p

- Mathematics
- 2015

We describe the image of general families of two-dimensional representations over compact semi-local rings. Applying this description to the family carried by the universal Hecke algebra acting on…

## References

SHOWING 1-10 OF 18 REFERENCES

### An infinite dimensional Hodge-Tate theory

- Mathematics
- 1993

L etG be the absolute Galois group of a p-adic field K and R a Banach algebra over K. Given a continuous homomorphism ρ : G→R ∗ (R ∗ = units of R) we construct a canonical operator ϕ ∈R ⊗K C which…

### Finite dimensional representations of algebras

- Mathematics
- 1974

Let R be a ring, K a field, and n a natural number. We will be concerned with the following type of questions: (a) Classify the representations of R in (hO, (or n dimensional representations). (b)…

### Deforming Galois Representations

- Mathematics
- 1989

Given a continuous homomorphism
$${G_{Q,S}}G{L_2}\left( {{Z_p}} \right)$$
where Gℚ,S is the Galois group of the maximal algebraic extension of ℚ unramified outside the finite set S of primes of…

### Generalized symmetric functions and invariants of matrices

- Mathematics
- 2008

We generalize the classical isomorphism between symmetric functions and invariants of a matrix. In particular, we show that the invariants over several matrices are given by the abelianization of the…

### On the characteristic polynomial of a sum of matrices

- Mathematics
- 1980

A formula is proved which relates the coefficients of the characteristic polynomial of a sum of matrices ΣtiAi with the coefficients of the characteristics polynomials in the monomials At1 …At, t⩽n.…

### A formula for the determinant of a sum of matrices

- Mathematics
- 1987

We give a formula, involving circular words and symmetric functions of the eigenvalues, for the determinant of a sum of matrices. Theorem of Hamilton-Cayley is deduced from this formula.

### Lois polynomes et lois formelles en théorie des modules

- Mathematics
- 1963

© Gauthier-Villars (Éditions scientifiques et médicales Elsevier), 1963, tous droits réservés. L’accès aux archives de la revue « Annales scientifiques de l’É.N.S. » (http://www.…