A scheme X is a topological space — which we denote by $|X|$ — and a sheaf of rings on the open subsets of $|X|$. We study the following natural but seldom considered questions. How to read off properties of $X$ from $|X|$? Does $|X|$ alone…
Categoria evento: Algebraic and Arithmetic Geometry Seminar
Brauer groups of moduli of hyperelliptic curves, via cohomological invariants – Roberto Pirisi (KTH Stockholm)
We use the theory of cohomological invariants for algebraic stacks to completely describe the Brauer group of the moduli stacks $H_g$ of genus $g$ hyperellitic curves over fields of characteristic zero, and the prime-to-$\mathsf{char}(k)$ part in…
Topological realization over $\mathbb{C}((t))$ via Kato-Nakayama spaces – Mattia Talpo (Università di Pisa)
I will report on some joint work with Piotr Achinger, about a “Betti realization” functor for varieties over the formal punctured disk $\mathsf{Spec}\mathbb{C}((t))$, i.e. defined by polynomials with coefficients in the field of formal Laurent…
Displaying the cohomology of toric line bundles – Klaus Altmann (Freie Universität Berlin)
Line bundles L on projective toric varieties can be understood as formal differences of convex polyhedra in the character lattice. We show how it is possible to use this language for understanding the cohomology of L by studying the set-theoretic…
Codimension two cycles and unramified third cohomology for certain products of two varieties – Jean-Louis Colliot-Thelene (Université de Paris-Saclay)
We investigate the integral Tate conjecture for 1-cycles on the product of a curve and a surface over a finite field, under the assumption that the surface is geometrically $\mathsf{CH}_0$-trivial. By this we mean that over any algebraically closed…
Cohomological Hall algebras – Francesco Sala (Università di Pisa)
The present talk is a gentle introduction to the theory of cohomological Hall algebras and their relevance in the study of the topology of moduli spaces, such as the Hilbert schemes of points on a smooth surface.…
The Beauville-Voisin conjecture for $\mathsf{Hilb}(K3)$ and the Virasoro algebra – Andrei Negut (MIT)
We give a geometric representation theory proof of a mild version of the Beauville-Voisin Conjecture for Hilbert schemes of $K3$ surfaces, namely the injectivity of the cycle map restricted to the subring of Chow generated by tautological classes.…
Triangulated categories of log-motives over a field – Federico Binda (Università di Milano Statale)
In this talk, I will give an overview of the construction of a triangulated category of motives for log smooth log schemes over a field $k$, based on the notion of finite log correspondence, in analogy to Voevodsky’s $\mathsf{DM}(k)$. The affine…
Anabelian representations of the motivic Galois group – Joseph Ayoub (University of Zurich)
TBA…
Decomposition along a non-linear flag – Gabriele Vezzosi (Università di Firenze)
We define a non-commutative version of the punctured formal neighborhood in algebraic geometry, and apply this construction to give decompositions of the (derived) stacks $\mathbf{Coh}^-(X)$, $\mathbf{Perf}(X)$, and $\mathbf{Bun}_G(X)$ along a…