We report on two classes of autoequivalences of the category of Yetter-Drinfeld modules over a finite group, or, equivalently the Drinfeld center of the category of representations of a finite group. Both operations are related to the r-th power operation, with r relatively prime to the exponent of the group. One is defined more generally for the group-theoretical fusion category defined by a f...

To a hyperbolic smooth curve defined over a number-field one naturally associates an "anabelian" representation of the absolute Galois group of the base field landing in outer automorphism group of the algebraic fundamental group. In this paper, we introduce several deformation problems for Lie-algebra versions of the above representation and show that, this way we get a richer structure than t...

Relations between the following classes of Galois extensions are given: (1) centrally projective Galois extensions (CP-Galois extensions), (2) faithfully Galois extensions, and (3) H-separable Galois extensions. Moreover, it is shown that the intersection of the class of CP-Galois extensions and the class of faithfully Galois extensions is the class of Azumaya Galois extensions.

Let p be a prime number and let n an integer not divisible by such that every group of order np has normal subgroup p. (This holds in particular for p>n.) Under these hypotheses, we obtain one-to-one correspondence between the isomorphism classes braces size set pairs (Bn,[τ]), where Bn runs over [τ] morphisms from multiplicative to Zp⁎ under certain equivalence relation. This gives classificat...

Let [Formula: see text] be a newform of even weight for text], where is possibly split indefinite quaternion algebra over text]. quadratic imaginary field splitting and an odd prime in We extend our theory text]-adic measures attached to the power series expansions around Galois orbit CM point corresponding embedding forms with any nebentypus dividing level For latter we restrict considerations...

Let V be a simple vertex operator algebra which admits the continuous, faithful action of a compact Lie group G of automorphisms. We establish a Schur-Weyl type duality between the unitary, irreducible modules for G and the irreducible modules for V G which are contained in V where V G is the space of G-invariants of V. We also prove a concomitant Galois correspondence between vertex operator s...

We generalise Coleman’s construction of Hecke operators to define an action of GL2(Ql) on the space of finite slope overconvergent p-adic modular forms (l 6= p). In this way we associate to any Cp-valued point on the tame level N Coleman-Mazur eigencurve an admissible smooth representation of GL2(Ql) extending the classical construction. Using the Galois theoretic interpretation of the eigencur...

The Langlands Program relates Galois representations and automorphic representations of reductive algebraic groups. The trace formula is a powerful tool in the study of this connection and the Langlands Functoriality Conjecture. After giving an introduction to the Langlands Program and its geometric version, which applies to curves over finite fields and over the complex field, I give a survey ...

In Remark 4.5 of [4] it is mentioned that there is a piece of the cohomology H(E) which has the same L-series as that of H3(Ṽ33). According to Tate’s conjecture there should be a correspondence between V33 and E . We give such a correspondence explicitly. Other relatives of these varieties are the fibered squares of the universal curves for Γ(3) and Γ0(9). In [8] and in the section 13 of [9] Sc...

We construct a functor from the category of p-adic étale local systems on a smooth rigid analytic variety X over a p-adic field to the category of vector bundles with an integrable connection on its “base change to BdR”, which can be regarded as a first step towards the sought-after p-adic Riemann-Hilbert correspondence. As a consequence, we obtain the following rigidity theorem for p-adic loca...