This is the first of a series of papers about quantization in the context of derived algebraic geometry. In this first part, we introduce the notion of n-shifted symplectic structures (n-symplectic… (More)

This is the first of a series of papers devoted to lay the foundations of Algebraic Geometry in homotopical and higher categorical contexts. In this first part we investigate a notion of higher… (More)

This is the second part of a series of papers called “HAG”, and devoted to develop the foundations of homotopical algebraic geometry. We start by defining and studying generalizations of standard… (More)

It is now well known that the K-theory of a Waldhausen category depends on more than just its (triangulated) homotopy category (see [20]). The purpose of this note is to show that the K-theory… (More)

We characterize ring spectra morphism from the algebraic cobordism spectrum MGL to an oriented spectrum E (in the sense of Morel [Mo]) via formal group laws on the ”topological” subring E∗ = ⊕iE 2i,i… (More)

We prove a decomposition theorem for the equivariant K-theory of actions of affine group schemes G of finite type over a field on regular separated noetherian algebraic spaces, under the hypothesis… (More)

In this note we present a work in progress whose main purpose is to establish a categorified version of sheaf theory. We present a notion of derived categorical sheaves, which is a categorified… (More)

The authors report on 28 patients with degenerative arthritis of the hip who underwent intertrochanteric osteotomy of the femur between 1970 and 1978. Two subjects were operated on bilaterally,… (More)