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One aspect of the Langlands program for linear groups is lifting of characters, which relates virtual representations on a group G with those on an endoscopic group for G. The goal of this paper is to...
In the absence of local lifting obstructions, the global obstruction lies in a Tate{Shafarevich group that can be analyzed via Tate duality. But we want more, namely to preserve local properties of ...
We study a coisometry that intertwines Popescu's presentations of minimal isometric dilations of a given operator tuple and of a coisometric lifting of the tuple. Using this we develop an outgoing Cun...
We extend the modularity lifting result of the arXiv:1111.2804 to allow Galois representations with some ramification at p. We also prove modularity mod 2 and 5 of certain Galois representations. We u...
It is proved that the Nagata automorphism (Nagata coordinates, respectively) of the polynomial algebra $F[x,y,z]$ over a field $F$ cannot be lifted to a $z$-automorphism ($z$-coordinate, respectively...
In [GN2] an effective solution of the lattice point counting problem in general domains in semisimple S-algebraic groups and affine symmetric varieties was established. The method relies on the mean e...
In this paper we generalize the notion of essential codimension of Brown, Douglas, and Fillmore using KK-theory and prove a result which asserts that there is a unitary of the form ‘identity + compac...
The critical point between varieties A and B of algebras is defined as the least cardinality of the semilattice of compact congruences of a member of A but of no member of B, if it exists.
Tropicalization is a procedure for associating a polyhedral complex to a subva-riety of an algebraic torus. We study the question on which graphs arise from tropicalizing algebraic curves. By using Ba...
Motivated by [1], we study on t-lifting modules (rings) and t-semiperfect modules (rings) for a preradical t and give some equivalent conditions. We prove that; i) if M is a projective t-lifting modul...

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