A Higher Dimensional Analogue of Mordell's Conjecture Over Function Fields.
A Hilbert-Mumford criterion for SL₂-actions
Let the special linear group G : = SL₂ act regularly on a ℚ-factorial variety X. Consider a maximal torus T ⊂ G and its normalizer N ⊂ G. We prove: If U ⊂ X is a maximal open N-invariant subset admitting a good quotient U → U ⃫N with a divisorial quotient space, then the intersection W(U) of all translates g · U is open in X and admits a good quotient W(U) → W(U) ⃫G with a divisorial quotient space. Conversely, we show that every maximal open G-invariant subset W ⊂ X admitting a good quotient W...
A Hirzebruch-Riemann-Roch formula for analytic spaces and non-projective algebraic varieties
A Hodge type decomposition for spinor valued forms
A home-made Hartshorne-Serre correspondence.
A homological criterion for reducibility of analytic spaces, with application to characterizing the theta divisor of a product of two general principally polarized abelian varieties.
A homological proof of a theorem by Davis, Geramita, Orecchia giving the Cayley-Bacharach theorem.
A Kummer criterion for imaginary quadratic fields
À la recherche de petites sommes d'exponentielles
Soit une fraction rationnelle à coefficients entiers, vérifiant des hypothèses assez générales. On prouve l’existence d’une infinité d’entiers , ayant exactement deux facteurs premiers, tels que la somme d’exponentielles soit en , où est une constante ne dépendant que de la géométrie de . On donne aussi des résultats de répartition du type Sato-Tate, pour certaines sommes de Salié, modulo , avec entier comme ci- dessus.
A Lax formalism for the elliptic difference Painlevé equation.
A Lefschetz decomposition for Chow motives of abelian schemes.
A limit linear series moduli scheme
We develop a new, more functorial construction for the basic theory of limit linear series, which provides a compactification of the Eisenbud-Harris theory. In an appendix, in order to obtain the necessary dimensional lower bounds on our limit linear series scheme we develop a theory of “linked Grassmannians”; these are schemes parametrizing sub-bundles of a sequence of vector bundles, which map into one another under fixed maps of the ambient bundles.
A linear bound on the t-normality of codimension two subvarieties of ...n.
A linear extension operator for Whitney fields on closed o-minimal sets
A continuous linear extension operator, different from Whitney’s, for -Whitney fields (p finite) on a closed o-minimal subset of is constructed. The construction is based on special geometrical properties of o-minimal sets earlier studied by K. Kurdyka with the author.
A local Bernstein inequality on real algebraic varieties.
A local-global principle for rational isogenies of prime degree
Let be a number field. We consider a local-global principle for elliptic curves that admit (or do not admit) a rational isogeny of prime degree . For suitable (including ), we prove that this principle holds for all , and for , but find a counterexample when for an elliptic curve with -invariant . For we show that, up to isomorphism, this is the only counterexample.
A look into the Severi varieties of curves in higher codimension.
A Mackey Imprimitivity Theory for Algebraic Groups.
A mathematical proof of a formula of Aspinwall and Morrison
A Measure for Semialgebraic Sets Related to Boolean Complexity.