Related papers: Reflection theorems for number rings

We answer a question posed by Y. Elias et al. in [8] about possible spectral distortions of algebraic numbers. We provide a closed form for the spectral distortion of certain classes of cyclotomic polynomials. Moreover, we present a bound…

The paper has been withdrawn, since there is a mistake in Proposition 5.2. The result on the telescope conjecture for semihereditary rings is correct, but the characterization of the smashing subcategories of the derived category of…

Andreev reflection at the interface between a ferromagnet and a superconductor has become a foundation of a versatile new technique of measuring the spin polarization of magnetic materials. In this paper we will briefly outline a general…

Over one year ago, a very long preprint posted on arXiv [arXiv:1709.03771] and HAL announced a proof of Lehmer's Conjecture (and of other related results). Unfortunately, as was remarked by several specialists, this proof contains a (at…

This short note is an erratum to arXiv:1306.4304, correcting the proof of one of its main results. It includes some counterexamples regarding infinite-dimensional unipotent groups and affine spaces that may be of independent interest.

We consider the reflected entropy and the associated entanglement spectrum for free fermions reduced to two intervals in 1+1 dimensions. Working directly in the continuum theory the reflected entropy can be extracted from the spectrum of a…

This paper is replaced by arXiv:1009.2490. The new paper includes a general impossibility result and restricted possibility results, and it has two additional authors.

The original version of the paper was published in Contemporary Mathematics 378 ``Groups, Languages, Algorithms''; 2005, pp. 319-348. This is a modified version with Appendix that holds a corrected formulation of Proposition 4.1.

The paper that was here is a preprint that was never turned into a proper paper. In particular it does not have enough citations to the literature. The paper "The Slice Algorithm For Irreducible Decomposition of Monomial Ideals" contains a…

These are notes of a series of lectures on mirror symmetry and topological string theory given at the Mathematical Sciences Center at Tsinghua University. The N=2 superconformal algebra, its deformations and its chiral ring are reviewed. A…

We consider fragments of uniform reflection for formulas in the analytic hierarchy over theories of second order arithmetic. The main result is that for any second order arithmetic theory $T_0$ extending ${\sf RCA}_0$ and axiomatizable by a…

The article is withdrawn. Its content is contained in the final version of arXiv:0805.1634.

This is an introduction to rings and fields, written for a quarter-long undergraduate course. It includes the basic properties of ideals, modules, algebras and polynomials, the constructions of ring extensions and finite fields, some…

This results in this paper have been merged with the result in arXiv:1003.0167. The authors would like to withdraw this version. Please see arXiv:1008.5356 for the merged version.

It is well-known that natural axiomatic theories are well-ordered by consistency strength. However, it is possible to construct descending chains of artificial theories with respect to consistency strength. We provide an explanation of this…

An improved (streamlined and extended) version of this paper is available as math.RA/0203010, which however omits some details. We recommend the later version unless details are essential.

This paper has been withdrawn pending revision.

The purpose of this paper is to prove that certain limits of polynomial rings are themselves polynomial rings, and show how this observation can be used to deduce some interesting results in commutative algebra. In particular, we give two…

A comment has been recently posted on the arXiv (arXiv:1902.07504) that discuss our recent work on encircling multiple exceptional points in Nat. Commun. 9, 4808 (2018). In that comment, the authors claim that our approach is prone to…

The proof given in the paper was incomplete due to an omission in the proof of Lemma 2. A corrected and improved version of the paper is in arXiv:0902.2486.