Géométrie algébrique et théorie des nombres en Bourgogne Franche-Comté

Contribution List

1. Full exceptional collections on Isotropic Grassmannians

Lyalya Guseva

3/28/25, 10:00 AM

The bounded derived category of coherent sheaves D(X) is an important invariant of an algebraic variety X. While the structure of derived categories is generally quite intricate, in certain cases when D(X) admits a so-called full exceptional collection, D(X) can be described explicitly. Some of the earliest examples of full exceptional collections were constructed by Kapranov in 1983 for...

2. La conjecture de Bloch-Kato et formes modulaires de poids 1

Arthur Gérard

3/28/25, 11:30 AM

Les formes modulaires de poids 1 et l'arithmétique des valeurs spéciales de fonction L semble assez mystérieuse. En effet, la fonction L de ces dernières ne possède pas de valeur critique au sens de Deligne, il semble alors nécessaire d'atteindre les formes modulaires de poids 1 par déformation p-adique, et le formalisme de la conjecture de Bloch-Kato se prête bien à cet exercice.
Dans cet...

3. (Relative)A1-Contractibility of Smooth Affine Schemes over a Dedekind base

Krishna Kumar Madhavan Vijayalakshmi

3/28/25, 12:00 PM

In 1935 Whitehead published a purported proof on Poincaré conjecture unveiling an homotopical obstruction to unique characterization of R^n among open contractible n-manifolds. However, it is now a fact that for all n>2, R^n is the unique open contractible n-manifold that is simply connected at infinity. The analogous question in algebraic geometry is to characterize the affine n-space among...

4. Les F-isocristaux comme connexions de de Rham-Witt

Rubén Muñoz–Bertrand

3/28/25, 2:00 PM

Les F-isocristaux sont des objets importants en cohomologie p-adique des variétés algébriques en caractéristique strictement positive. Ceux-ci viennent avec une action du Frobenius qui induit un endomorphisme sur la cohomologie. Jusqu'à présent, la construction de ces objets et du Frobenius faisait intervenir soit des catégories de Grothendieck, soit des faisceaux sur lesquels on ne peut pas,...

5. Enumerative geometry using motivic theory

Victor Chachay

3/28/25, 3:30 PM

When computing enumerative invariants on algebraic surfaces, one often has to work over an algebraically closed field. We will use an example to highlight the problems on other fields and how the motivic theory is a way to go around it.

6. The method of Eisenstein congruences in Iwasawa theory.

Ruichen Xu

3/28/25, 4:00 PM

In Iwasawa theory, people study the mysterious relations between special values of L-functions and arithmetic objects (such as certain Galois cohomology groups called Selmer groups) as they vary in p-adic families. These relationships are formulated as the Iwasawa main conjectures. Among the successful approaches to these conjectures, one divisibility of them, namely “the lower bound of Selmer...