相关论文: An index theorem for gerbes

This note offers an elementary proof of the Siegel-Walfisz theorem for primes in arithmetic progressions.

We prove an index theorem for families of linear periodic Hamiltonian systems, which is reminiscent of the Atiyah-Singer index theorem for selfadjoint elliptic operators. For the special case of one-parameter families, we compare our…

We give a new proof of the butterfly theorem, based on the use of several expressions involving the scale factor between the two wings.

We construct geometrically a gerbe assigned to a connection on a principal SU(2)-bundle over an oriented closed 1-dimensional manifold. If the connection is given by the restriction of a connection on a bundle over a compact 2-manifold…

We give in the present work a new methodology that allows to give isoperimetric proofs, for Kneser's Theorem and Kemperman's structure Theory and most sophisticated results of this type. As an illustration we present a new proof of Kneser's…

We prove an analogue of the fixed-point theorem for the case of definably amenable groups.

An index transform, involving the square of Whittaker's function is introduced and investigated. The corresponding inversion formula is established. Particular cases cover index transforms of the Lebedev type with products of the modified…

Discrete analogs of the index transforms, involving Bessel and the modified Bessel functions are introduced and investigated. The corresponding inversion theorems for suitable classes of functions and sequences are established.

We prove a new theorem on additive Levy processes and show that this theorem implies several proved theorems and a hard conjectured theorem.

In this paper, among other things, we state and prove the mean ergodic theorem for amenable semigroup algebras.

The Butterfly Theorem is explored in Taxicab Geometry.

In this short note a new proof of the monotone con- vergence theorem of Lebesgue integral on \sigma-class is given.

In this paper, we prove a local equivariant index theorem for sub-signature operators which generalizes the Zhang's index theorem for sub-signature operators.

In this paper, we prove a semistable reduction type theorem for multi-filtered vector spaces (or known as multi-weighted vector spaces).

In this paper, we would like to propose a fundamental question about a higher dimensional analogue of Dirichlet's unit theorem. We also give a partial answer to the question as an application of the arithmetic Hodge index theorem.

We present infinite analogues of our splinter lemma from [Trees of tangles in abstract separation systems, arXiv:1909.09030]. From these we derive several tree-of-tangles-type theorems for infinite graphs and infinite abstract separation…

An algebraic deformation theory of coalgebra morphisms is constructed.

We propose to interpret Levinson's theorem as an index theorem. This exhibits its topological nature. It furthermore leads to a more coherent explanation of the corrections due to resonances at thresholds.

We prove the Identity Theorem for pro-$p$-groups with a single defining relation giving a positive feedback to a question of Serre on the structure of relation modules. A construction of "conjurings" indicates finality of our result in a…

We prove a Noether-Deuring theorem for the derived category of bounded complexes of modules over a Noetherian algebra.