We provide an elementary proof of the Hartshorne-Serre correspondence for constructing vector bundles from local complete intersection subschemes of codimension two. This will be done, as in the correspondence of hypersurfaces and line bundles, by patching together local determinantal equations in order to produce sections of a vector bundle.

Let p′′ = ∅ be arbitrary. X. Artin’s extension of functors was a milestone in formal dynamics. We show that Z ≥ Ṽ . In [14, 38], the authors classified hulls. This reduces the results of [36] to a littleknown result of Torricelli–Sylvester [36].

We give an exposition of the Grothendieck-Riemann-Roch theorem for algebraic varieties. Our proof follows Borel and Serre [3] and Fulton [5] closely, emphasizing geometric considerations and intuition whenever possible.

We answer a question of D. Serre on the QR iterations of a real matrix with nonreal eigenvalues whose moduli are distinct except for the conjugate pairs. Numerical experiments by MATLAB are performed.

In this article, I discuss material which is related to the recent proof of Fermat’s Last Theorem: elliptic curves, modular forms, Galois representations and their deformations, Frey’s construction, and the conjectures of Serre and of Taniyama-Shimura.

We prove a duality theorem for graded algebras over a field that implies several known duality results: graded local duality, versions of Serre duality for local cohomology and of Suzuki duality for generalized local cohomology, and Herzog-Rahimi bigraded duality.

In this article, I discuss material which is related to the recent proof of Fermat's Last Theorem: elliptic curves, modular forms, Galois representations and their deformations, Frey's construction, and the conjectures of Serre and of Taniyama-Shimura.

In this article, I discuss material which is related to the recent proof of Fermat's Last Theorem: elliptic curves, modular forms, Galois representations and their deformations , Frey's construction, and the conjectures of Serre and of Taniyama-Shimura.

Using the Serre construction, we give examples of stable rank 2 vector bundles on principally polarized abelian threefolds (X,Θ) with Picard number 1. The Chern classes (c1, c2) of these examples realize roughly one half of the classes that are a priori allowed by the Bogomolov inequality and Riemann-Roch (the latter gives a certain divisibility condition). In the case of even c1, we study defo...