Related papers: Extended eigenvarieties for overconvergent cohomol…

We present a comprehensive study of the geometry of Hilbert $p$-adic eigenvarieties at classical parallel weight one intersection points of their cuspidal and Eisenstein loci. For instance, we determine all such points at which the weight…

Equivariant compactifications of reductive groups can be described by combinatorial data. On the other hand, equivariant compactifications of the additive group G^n_a are more complicated in at least two respects. First, they often admit…

In this paper, we associate Galois representations to globally generic cuspidal automorphic representations on GSp(4), over a totally real field F, which are Steinberg at some finite place. This association is compatible with the local…

Let $L$ be a finite extension of $\mathbb{Q}_p$. We calculate the dimension of $\text{Ext}^1$-groups of certain locally analytic representations of $\text{GL}_2(L)$ defined using coherent cohomology of Drinfeld curves. Furthermore, let…

We extend the lifting methods of our previous paper to lift reducible odd representations $\bar{\rho}:\mathrm{Gal}(\overline{F}/F) \to G(k)$ of Galois groups of global fields $F$ valued in Chevalley groups $G(k)$. Lifting results, when…

We give a new construction of $p$-adic overconvergent Hilbert modular forms by using Scholze's perfectoid Shimura varieties at infinite level and the Hodge--Tate period map. The definition is analytic, closely resembling that of complex…

We study the moduli of G-local systems on smooth but not necessarily proper complex algebraic varieties. We show that, when suitably considered as derived algebraic stacks, they carry natural Poisson structures, generalizing the well known…

We introduce a natural map from the space of pure-type complex differential forms on a complex manifold to the corresponding one on the infinitesimal deformations of this complex manifold. By use of this map, we generalize an extension…

We study (non-abelian) extensions of a given super Lie algebra, identify a cohomological obstruction to the existence, parallel to the known one for Lie algebras. An analogy to the setting of covariant exterior derivatives, curvature, and…

We quantize the generalized-Witt algebra in characteristic 0 with its Lie bialgebra structures discovered by Song-Su (\cite{GY}). Via a modulo p reduction and a modulo "p-restrictedness" reduction process, we get 2^n{-}1 families of…

Let G be a connected, real, semisimple Lie group contained in its complexification G_C, and let K be a maximal compact subgroup of G. We construct a K_C-G double coset domain in G_C, and we show that the action of G on the K-finite vectors…

For a compact space X we consider extending endomorphisms of the algebra C(X) to be endomorphisms of Arens-Hoffman and Cole extensions of C(X). Given a non-linear, monic polynomial p in C(X)[t], with C(X)[t]/pC(X)[t] semi-simple, we show…

We interpolate the Gauss-Manin connection in p-adic families of nearly overconvergent modular forms. This gives a family of Maass-Shimura type differential operators from the space of nearly overconvergent modular forms of type r to the…

We develop a construction of the unitary type anti-involution for the quantized differential calculus over $GL_q(n)$ in the case $|q|=1$. To this end, we consider a joint associative algebra of quantized functions, differential forms and…

We prove that the classical algebraic varieties over algebraically closed fields can be defined over arbitrary fields $k.$ Then we prove that for associative algebras $A$, there exist local representing objects $A_M$ for simple modules $M.$…

In Remarks on Galois Cohomology and Definability [2], Pillay introduced definable Galois cohomology, a model-theoretic generalization of Galois cohomology. Let $M$ be an atomic and strongly $\omega$-homogeneous structure over a set of…

We review (non-abelian) extensions of a given Lie algebra, identify a 3-dimensional cohomological obstruction to the existence of extensions. A striking analogy to the setting of covariant exterior derivatives, curvature, and the Bianchi…

We give a purely algebraic construction of a cohomological field theory associated with a quasihomogeneous isolated hypersurface singularity W and a subgroup G of the diagonal group of symmetries of W. This theory can be viewed as an…

we construct infinitely many non-isotrivial families of abelian varieties of $GL_2$-type over four punctured projective lines with bad reduction of type-$(1/2)_\infty$ via $p$-adic Hodge theory and Langlands correspondence. They lead to…

We prove an unconditional power saving for the dimension of the space of cohomological automorphic forms of fixed level and growing weight on GL_2 over any number field which is not totally real. Our proof involves the theory of p-adically…