p-adic variations of automorphic sheaves
Freitag, 11.1.19, 10:30-11:30, Raum 404, Ernst-Zermelo-Str. 1
Elliptic modular forms are a special kind of functions on the Poincare' upper half space and have played an increasingly important role in modern Number Theory. Starting with the works of J.P. Serre and N. Katz more than 30 years ago, it was discovered that, given a prime number p, such modular forms have also a p-adic nature and, especially, live in p-adic families. This phenomenon is the counterpart of the theory fo p-adic deformations of Galois representations and has become a basic tool for number theorists. I will present joint work with A. Iovita and V. Pilloni providing a geometric explanation of this, purely p-adic, phenomenon.\n
Computing classes of admissible covers
Freitag, 18.1.19, 10:30-11:30, Raum 404, Ernst-Zermelo-Str. 1
Let Adm(g,h,G) be the space of degree admissible G covers C → D of a genus h curve D by genus g curves C. There is a natural map f : Adm(g,h,G) → Mgnbar into the moduli space of stable curves taking the source curve of an admissible cover and forgetting everything else. When the class [f(Adm(g,h,G))] is tautological we can try to express this class in terms of a known basis for the tautological ring of Mgnbar. We will discuss several strategies for making these computations and give a number of examples.\n
Rigidity for equivariant K-theory
Freitag, 25.1.19, 10:30-11:30, Raum 404, Ernst-Zermelo-Str. 1
This talk is a report on joint work with Jeremiah Heller and Paul Arne Østvær. The Gabber-Gillet-Thomason rigidity theorem asserts that the natural map from a henselian local ring to its residue field induces an isomorphism on algebraic K-theory with finite coefficients (coprime to the exponential characteristic). We establish a version of this rigidity theorem in the setting of homotopy invariant equivariant pseudo pretheories of smooth schemes over a field with an action of a finite group. Examples include equivariant algebraic K-theory and presheaves with equivariant transfers.