Inheritance Bazex-Dupré-Christol syndrome is an X-linked dominant genodermatosis, with a prevalence below 1/1 000 000. The female to male ratio reaches the expected 2:1, and females appear to be less affected than males. There is intrafamilial and interfamilial phenotypic variability (Lacombe and Taïeb, 1995; Kidd et al., 1996). Most cases are European patients. Oley syndrome (Oley et al., 1992...

Bazex-Dupre-Christol (BDC) syndrome is clinically characterizedby multiple basal cell carcinomas of the face that mainly occurduring the second and third decade of life, follicular atrophodermapredominantly of the dorsum sides of the hands and feetand generalized hypotrichosis; sometimes with pili torti andtrichorrhexis nodosa. Features commonly associated with BDCare milia, hypohidrosis and ca...

Abstract Linked Article: Liu et al. Br J Dermatol 2022; 187:948–961.

This primarily expository article collects together some facts from the literature about the monodromy of differential equations on a p-adic (rigid analytic) annulus, though often with simpler proofs. These include Matsuda’s classification of quasiunipotent ∇-modules, the Christol-Mebkhout construction of the ramification filtration, and the Christol-Dwork Frobenius antecedent theorem. We also ...

Bazex-Dupre-Christol syndrome (BDCS) is an X linked dominant disorder of the hair follicle characterised by follicular atrophoderma, multiple basal cell carcinomas, hypotrichosis, milia, and localised hypohidrosis. Follicular atrophoderma (FA) are follicular funnel shaped depressions, "ice pick marks", seen most commonly on the dorsum of the hands. We describe the first known Scottish family wi...

We give algebraic proofs of transcendence over Q(X) of formal power series with rational coeecients, by using inter alia reduction modulo prime numbers, and the Christol theorem. Applications to generating series of languages and combinatorial objects are given.

In the vein of Christol, Kamae, Mendès France and Rauzy, we consider the analogue of a problem of Mahler for rational functions in positive characteristic. To solve this question, we prove an extension of Cobham’s theorem for quasi-automatic functions and use the recent generalization of Christol’s theorem obtained by Kedlaya.  2008 Elsevier Inc. All rights reserved.