We compute the unramified cohomology of quadrics of dimension 4 in degree 4 over an arbitrary field of characteristic different from 2. We find that it is related to classical invariants of a more elementary nature, such as the group of spinor norms and the projective special orthogonal group modulo Manin’s R-equivalence.

For n ≥ k, an (n, k, d)q-code C is a collection of q n-tuples (or codewords) over an alphabet A of size q such that the minimum (Hamming) distance between any two codewords of C is d. For such a code, the Singleton bound (|C| ≤ |A|n−d+1) gives d ≤ n− k + 1. The Singleton defect of C, S(C), is defined by S(C) = n− k + 1− d. A code C ′ obtained by deleting some fixed coordinate from each codeword...

For any smooth connected linear algebraic group G $G$ over an algebraically closed field k $k$ , we describe the Picard of universal moduli stack principal -bundles pointed -projective curves.

Characterizing the universal coverings of smooth projective varieties is an old and hard question. Central to the subject is a conjecture of Shafarevich according to which the universal cover X̃ of a smooth projective variety is holomorphically convex, meaning that for every infinite sequence of points without limit points in X̃ there exists a holomorphic function unbounded on this sequence. In t...

A general framework for integration over certain infinite dimensional spaces is first developed using projective limits of a projective family of compact Hausdorff spaces. The procedure is then applied to gauge theories to carry out integration over the non-linear, infinite dimensional spaces of connections modulo gauge transformations. This method of evaluating functional integrals can be used...

A general framework for integration over certain innnite dimensional spaces is rst developed using projective limits of a projective family of compact Hausdorr spaces. The procedure is then applied to gauge theories to carry out integration over the non-linear, innnite dimensional spaces of connections modulo gauge transformations. This method of evaluating functional integrals can be used eith...

We show, in full generality, that Lusztig’s a-function describes the projective dimension of both indecomposable tilting modules and indecomposable injective modules in the regular block of the BGG category O, proving a conjecture from the first paper. On the way we show that the images of simple modules under projective functors can be represented in the derived category by linear complexes of...

We propose fully explicit projective integration and telescopic schemes for the multispecies Boltzmann Bhatnagar-Gross-Krook (BGK) equations. The methods employ a sequence of small forward-Euler steps, intercalated with large extrapolation steps. approach repeats said extrapolations as basis an even larger step. This hierarchy renders computational complexity method essentially independent stif...