A smooth, oriented n-manifold is called a homotopy sphere if it is homeomorphic, but not necessarily diffeomorphic, to the standard n-sphere. In dimensions n>4

, one often studies the group Θn of homotopy spheres up to orientation-preserving...

Workshop on p-adic Arithmetic Geometry

A smooth, oriented n-manifold is called a homotopy sphere if it is homeomorphic, but not necessarily diffeomorphic, to the standard n-sphere. In dimensions n>4

, one often studies the group Θn of homotopy spheres up to orientation-preserving...

In chromatic homotopy theory, an object like the sphere spectrum S0

is studied by means of its "localizations", much as an abelian group can be localized at each prime p. Remarkably, the "primes" K(n)

in the homotopy setting correspond to formal...

In joint work in progress with Anschütz and Le Bras we aim to construct a 6-functor formalism for quasicoherent sheaves on the relative Fargues-Fontaine curve over rigid-analytic varieties (and even general v-stacks), providing new insights into the...

The recent work of Drinfeld and Bhatt-Lurie led to a new geometric approach to p-adic cohomology theories, analogously to what was done earlier in Hodge theory by Simpson. This stacky perspective gives in particular a new approach to p-adic non...

With every bounded prism Bhatt and Scholze associated a cohomology theory of formal p-adic schemes. The prismatic cohomology comes equipped with the Nygaard filtration and the Frobenius endomorphism. The Bhatt-Scholze construction has been advanced...

I will talk about (very much in progress) joint work with Mark Kisin on a Hodge—Newton style inequality for the mod p Breuil—Kisin modules arising from crystalline Galois representations.

The minimal model program for 3-folds has been developed only in characteristics p greater than or equal to 5. A key difficulty at small primes is that the singularities occurring in the minimal model program need not be Cohen-Macaulay, as they are...

Let f:Y→X be a finite covering map of complex algebraic varieties. The essential dimension of f is the smallest integer e such that, birationally, f arises as the pullback of a covering Y′→X′

of dimension e, via a map X→X′. This invariant goes back...

A theorem of Borel says that any holomorphic map from a complex algebraic variety to a smooth arithmetic variety is automatically an algebraic map. The key ingredient is to show that any holomorphic map from the (poly) punctured disc to the Baily...

Let E be a finite degree extension of Qp. Given a mod p representation of the absolute Galois group of E we construct a sheaf on a punctured absolute Banach-Colmez space that should give the first step in the construction of the mod p local Langlands...