We state a result and describe an algorithm for computing the intersection number between abelian varieties associated to complementary subspaces of the space of cuspidal modular forms.

We construct an endoscopic decomposition for local L-packets associated to irreducible cuspidal Deligne–Lusztig representations. Moreover, the obtained decomposition is compatible with inner twistings.

For any convex preorder on the set of positive roots affine type A, we classify and construct all associated cuspidal semicuspidal skew shapes. These combinatorial objects correspond to Specht modules for Khovanov-Lauda-Rouquier algebra A. Cuspidal shapes are ribbons, show that every shape has a unique ordered tiling by ribbons. This data provides an upper bound, in bilexicographic order Kostan...

We construct an endoscopic decomposition for local L-packets associated to irreducible cuspidal Deligne-Lusztig representations. Moreover, the obtained decomposition is compatible with inner twistings.

— We construct a rigid-analytic map from the the author’s half-integral weight cuspidal eigencurve (see [10]) to its integral weight counterpart that interpolates the classical Shimura lifting.

let $a$ be an abelian topological group and $b$ a trivial topological $a$-module. in this paper we define the second bilinear cohomology with a trivial coefficient. we show that every abelian group can be embedded in a central extension of abelian groups with bilinear cocycle. also we show that in the category of locally compact abelian groups a central extension with a continuous section can b...

in this paper, we consider a class of connected oriented (with respect to z/p) closed g-manifolds with a non-empty finite fixed point set, each of which is g-equivariantly formal, where g = z/p and p is an odd prime. using localization theorem and equivariant index, we give an explicit description of the mod p equivariant cohomology ring of such a g-manifold in terms of algebra. this makes it p...

Let R be a commutative Noetherian ring, I an ideal of R and M a non-zero R-module. In this paper we calculate the extension of annihilator of local cohomology modules H^t_I(M), t≥0, under the ring extension R⊂R[X] (resp. R⊂R[[X]]). By using this extension we will present some of the faithfulness conditions of local cohomology modules, and show that if the Lynch's conjecture, i...