Triunfo ó ruina infalible de las Cortes Generales y Extraordinarias : discurso presentado a las mismas Cortes el día 14 de Enero de 1811 para la elección de su futura suerte por D. J. de M

Reimp. de la ed. de: Cádiz : Antonio Murguia, 1811

El Real Gabinete Topográfico del Buen Retiro (1832-1854)

El Real Gabinete Topográfico del Buen Retiro (1832-1854

Sagunt (València). Sitios. 1811

Inscripción en ángulo inferior derecho: "Nota: Les Chiffres entre Parenthèses indiquent les Cotes de Nivellement..."

Calendario para el Reyno de Valencia...: Año 1832

Microfilme. Valencia: BV, ca. 1990

Adjoint modular Galois representations and their Selmer groups

In the last 15 years, many class number formulas and main conjectures have been proven. Here, we discuss such formulas on the Selmer groups of the three-dimensional adjoint representation ad(φ) of a two-dimensional modular Galois representation φ. We start with the p-adic Galois representation φ0 of a modular elliptic curve E and present a formula expressing in terms of L(1, ad(φ0)) the intersection number of the elliptic curve E and the complementary abelian variety inside the Jacobian of the modular curve. Then we explain how one can deduce a formula for the order of the Selmer group Sel(ad(φ0)) from the proof of Wiles of the Shimura–Taniyama conjecture. After that, we generalize the formula in an Iwasawa theoretic setting of one and two variables. Here the first variable, T, is the weight variable of the universal p-ordinary Hecke algebra, and the second variable is the cyclotomic variable S. In the one-variable case, we let φ denote the p-ordinary Galois representation with values in GL2(Zp[[T]]) lifting φ0, and the characteristic power series of the Selmer group Sel(ad(φ)) is given by a p-adic L-function interpolating L(1, ad(φk)) for weight k + 2 specialization φk of φ. In the two-variable case, we state a main conjecture on the characteristic power series in Zp[[T, S]] of Sel(ad(φ) ⊗ ν−1), where ν is the universal cyclotomic character with values in Zp[[S]]. Finally, we describe our recent results toward the proof of the conjecture and a possible strategy of proving the main conjecture using p-adic Siegel modular forms.

Deforming semistable Galois representations

Let V be a p-adic representation of Gal(Q̄/Q). One of the ideas of Wiles’s proof of FLT is that, if V is the representation associated to a suitable autromorphic form (a modular form in his case) and if V′ is another p-adic representation of Gal(Q̄/Q) “closed enough” to V, then V′ is also associated to an automorphic form. In this paper we discuss which kind of local condition at p one should require on V and V′ in order to be able to extend this part of Wiles’s methods.

On degree 2 Galois representations over

We discuss proofs of some new special cases of Serre’s conjecture on odd, degree 2 representations of Gℚ.

A secret sharing scheme based on exponentiation in Galois fields

To provide more efficient and flexible alternatives for the applications of secret sharing schemes, this paper describes a threshold sharing scheme based on exponentiation of matrices in Galois fields. A significant characteristic of the proposed scheme is that each participant has to keep only one master secret share which can be used to reconstruct different group secrets according to the number of threshold values.

Letter to William Croswell, 1811 May 23

Two-page letter from an individual with advice about Croswell's future publishing activities. The correspondent's signature is illegible.

Letter from William Croswell to John C. Page, 1811 December 24

Draft of a one-page letter regarding Page's financial assistance to Croswell in Liverpool, with a laid-in leaf containing an accounting statement.

Letter from William Croswell to the Masters of Mason Street Schools, 1832 March 8

Draft of a brief letter complaining about students.

Letter from William Croswell to Sarah C. Bumstead, 1832 September 10

Brief letter concerning the repayment of a loan.