In Carayol’s note [4], a geometric construction of the Galois representations associated to Hilbert modular forms and the compatibility with the local Langlands correspondence are discussed. In loc. cit., the compatibility is established in the case = p where the Galois representation is an -adic representation and p is the prime divided by the prime p of the totally real field where the restri...

J Metz, T Lahaye, B Fröhlich, A Griesmaier, T Pfau, H Saito, Y Kawaguchi, and M Ueda 5. Physikalisches Institut, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany Department of Applied Physics and Chemistry, The University of Electro-Communications, Tokyo 182-8585, Japan Department of Physics, University of Tokyo, Tokyo 113-033, Japan and ERATO Macroscopic Quantum Project, JST...

Using n finite order automorphisms on a simple complex Lie algebra we construct twisted n-toroidal Lie algebras. Thus obtaining Lie algebras wich have a rootspace decomposition. For the case n = 2 we list certain simple Lie algebras and their automorphisms, which produce twisted 2-toroidal algebras. In this way we obtain Lie algebras that are related to all Extended Affine Root Systems of K. Sa...

We give a Hodge-theoretic interpretation of the multi-plier ideal of an effective divisor on a smooth complex variety. More precisely, we show that the associated graded coherent sheaf with respect to the jumping-number filtration can be recovered from the smallest piece of M. Saito's Hodge filtration of the D-module of vanishing cycles.

M. Hirai, ∗ S. Kumano, 2, † and N. Saito ‡ (Asymmetry Analysis Collaboration) Institute of Particle and Nuclear Studies High Energy Accelerator Research Organization (KEK) 1-1, Ooho, Tsukuba, Ibaraki, 305-0801, Japan Department of Particle and Nuclear Studies The Graduate University for Advanced Studies 1-1, Ooho, Tsukuba, Ibaraki, 305-0801, Japan Department of Physics, Kyoto University, Kyoto,...

We give another proof of a theorem of H. Kajiura, K. Saito, and A. Takahashi [9] based on the theory of weighted projective lines by Geigle and Lenzing [5, 6] and a theorem of Orlov [13] on triangulated categories of graded B-branes. The content of this paper appears in the appendix to math.AG/0511155.

The module of derivations D(1)(A) of a hyperplane arrangement A ∈ C (henceforth called an n-arrangement) is an interesting and much studied object [10, 9, 8]. In particular, the question whether this module is free, for various classes of arrangements, has received great attention. On the other hand, the module of higher differential operators D(m)(A) received their first incisive treatment in ...

Trivia: in how many different ways can the log canonical threshold of a polynomial be computed? At least six ways in general, plus four more ways with some luck. This richness of approaches reflects the central place that log canonical thresholds and, more generally, multiplier ideals have in singularity theory. Singularity theory is a subject deeply connected with many areas of mathematics and...

We show that the p-adic Galois representations attached to Hilbert modular forms of motivic weight are potentially semistable at all places above p and are compatible with the local Langlands correspondence at these places, proving this for those forms not covered by the previous works of T. Saito and of D. Blasius and J. Rogawski. 2000 Mathematics Subject Classification: 11F80, 11F41