1,721,002 research outputs found
Cohomological invariants of genus three hyperelliptic curves
Full text linkWe compute the cohomological invariants with coefficients in Z/pZ of the stack H3 of hyperelliptic curves of genus 3 over an algebraically closed field
Cohomological invariants of hyperelliptic curves of even genus
Full text linkLet g be an even positive integer, and let p be a prime number. We compute the cohomological invariants with coefficients in Z/pZ of the stacks of hyperelliptic curves Hg over an algebraically closed field k0
Cohomological Invariants for stacks of algebraic curves
Full text linkNon UBCUnreviewedAuthor affiliation: University of OttawaPostdoctora
On the motivic class of the classifying stack of G-2$ and the spin groups
Full text linkWe compute the class of the classifying stack of the exceptional algebraic group G2 and of the spin groups Spin7 and Spin8 in the Grothendieck ring of stacks, and show that they are equal to the inverse of the class of the corresponding group. Furthermore, we show that the computation of the motivic classes of the stacks BSpinn can be reduced to the computation of the classes of Bn, where n δ Pinn is the "extraspecial 2-group", the preimage of the diagonal matrices under the projection Pinn δ On to the orthogonal group
Gabriel's theorem and birational geometry
Full text linkExtending work of Meinhardt and Partsch, we prove that two varieties are isomorphic away from a subset of a given dimension if and only if certain quotients of their categories of coherent sheaves are equivalent. This result interpolates between Gabriel's reconstruction theorem and the fact that two varieties are birational if and only if they have the same function field
Cohomological invariants of root stacks and admissible double coverings
No full textWe give a formula for the cohomological invariants of a root stack, which we apply to compute the cohomological invariants and the Brauer group of the compactification of the stacks of hyperelliptic curves given by admissible double coverings
Brauer groups of moduli of hyperelliptic curves via cohomological invariants
Full text linkUsing the theory of cohomological invariants for algebraic stacks, we compute the Brauer group of the moduli stack of hyperelliptic curves over any field of characteristic. In positive characteristic, we compute the part of the Brauer group whose order is prime to the characteristic of the base field
The Picard Group of the Universal Abelian Variety and the Franchetta Conjecture for Abelian Varieties
No full textWe compute the Picard group of the universal Abelian variety over the moduli stack Ag,n of principally polarized Abelian varieties over C with a symplectic principal level n-structure. We then prove that over C the statement of the Franchetta conjecture holds in a suitable form for Ag,n
A Complete Description of the Cohomological Invariants of Even Genus Hyperelliptic Curves
Full text linkWhen the genus g is even, we extend the computation of mod 2 cohomological invariants of Hgto non algebraically closed fields, we give an explicit functorial description of the invariants and we completely describe their multiplicative structure. In the Appendix, we show that the cohomological invariants of the compactification (Formula presented)gare trivial, and use our methods to give a very short proof of a result by Cornalba on the Picard group of the compactification (Formula presented)gand extend it to positive characteristic
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