scholarly journals Brauer groups of moduli of hyperelliptic curves via cohomological invariants

2021 ◽  
Vol 9 ◽  
Author(s):  
Andrea Di Lorenzo ◽  
Roberto Pirisi
Keyword(s):  
Positive Characteristic ◽  
Hyperelliptic Curves ◽  
Brauer Group ◽  
Base Field ◽  
Brauer Groups ◽  
Algebraic Stacks ◽  
Cohomological Invariants ◽  
Moduli Stack

Abstract Using the theory of cohomological invariants for algebraic stacks, we compute the Brauer group of the moduli stack of hyperelliptic curves ${\mathcal {H}}_g$ over any field of characteristic $0$ . In positive characteristic, we compute the part of the Brauer group whose order is prime to the characteristic of the base field.

A Note on the Height of the Formal Brauer Group of a K3 Surface

2004 ◽  
Vol 47 (1) ◽  
pp. 22-29 ◽  
Author(s):  
Yasuhiro Goto
Keyword(s):  
Positive Characteristic ◽  
Brauer Group ◽  
K3 Surface ◽  
Brauer Groups

AbstractUsing weighted Delsarte surfaces, we give examples of K3 surfaces in positive characteristic whose formal Brauer groups have height equal to 5, 8 or 9. These are among the four values of the height left open in the article of Yui [11].

scholarly journals Finiteness of Brauer groups of K3 surfaces in characteristic 2

2018 ◽  
Vol 14 (06) ◽  
pp. 1813-1825
Author(s):  
Kazuhiro Ito
Keyword(s):  
K3 Surfaces ◽  
Torsion Subgroup ◽  
Brauer Group ◽  
Base Field ◽  
Brauer Groups ◽  
Finitely Generated ◽  
Tate Conjecture ◽  
Characteristic 2 ◽  
Primary Torsion

For a [Formula: see text] surface over a field of characteristic [Formula: see text] which is finitely generated over its prime subfield, we prove that the cokernel of the natural map from the Brauer group of the base field to that of the [Formula: see text] surface is finite modulo the [Formula: see text]-primary torsion subgroup. In characteristic different from [Formula: see text], such results were previously proved by Skorobogatov and Zarhin. We basically follow their methods with an extra care in the case of superspecial [Formula: see text] surfaces using the recent results of Kim and Madapusi Pera on the Kuga-Satake construction and the Tate conjecture for [Formula: see text] surfaces in characteristic [Formula: see text].

TWO-TORSION OF THE BRAUER GROUPS OF HYPERELLIPTIC CURVES AND UNRAMIFIED ALGEBRAS OVER THEIR FUNCTION FIELDS

2001 ◽  
Vol 29 (9) ◽  
pp. 3971-3987 ◽  
Author(s):  
U. Rehmann ◽  
S. V. Tikhonov ◽  
V. I. Yanchevskii
Keyword(s):  
Function Fields ◽  
Hyperelliptic Curves ◽  
Brauer Groups

scholarly journals THE 2-RANKS OF HYPERELLIPTIC CURVES WITH EXTRA AUTOMORPHISMS

2009 ◽  
Vol 05 (05) ◽  
pp. 897-910 ◽  
Author(s):  
DARREN GLASS
Keyword(s):  
Automorphism Group ◽  
Hyperelliptic Curve ◽  
Hyperelliptic Curves ◽  
Closed Field ◽  
Base Field ◽  
Characteristic P ◽  
Algebraically Closed Field ◽  
Characteristic Two ◽  
Carry Over ◽  
The Relationship

This paper examines the relationship between the automorphism group of a hyperelliptic curve defined over an algebraically closed field of characteristic two and the 2-rank of the curve. In particular, we exploit the wild ramification to use the Deuring–Shafarevich formula in order to analyze the ramification of hyperelliptic curves that admit extra automorphisms and use this data to impose restrictions on the genera and 2-ranks of such curves. We also show how some of the techniques and results carry over to the case where our base field is of characteristic p > 2.

scholarly journals Introduction to the Ekedahl Invariants

2017 ◽  
Vol 120 (2) ◽  
pp. 211 ◽  
Author(s):  
Ivan Martino
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Algebraic Stacks ◽  
Cohomological Invariants ◽  
Equivalent Definition ◽  
A Finite Group

In 2009, T. Ekedahl introduced certain cohomological invariants for finite groups. In this work we present these invariants and we give an equivalent definition that does not involve the notion of algebraic stacks. Moreover we show certain properties for the class of the classifying stack of a finite group in the Kontsevich value ring.

scholarly journals DUALITY FOR COHOMOLOGY OF CURVES WITH COEFFICIENTS IN ABELIAN VARIETIES

2018 ◽  
Vol 240 ◽  
pp. 42-149 ◽  
Author(s):  
TAKASHI SUZUKI
Keyword(s):  
Function Field ◽  
Positive Characteristic ◽  
Abelian Varieties ◽  
Base Field ◽  
Tate Pairing ◽  
Global Function ◽  
Crystalline Cohomology ◽  
Local Duality ◽  
Height Pairing ◽  
Finite Base

In this paper, we formulate and prove a duality for cohomology of curves over perfect fields of positive characteristic with coefficients in Néron models of abelian varieties. This is a global function field version of the author’s previous work on local duality and Grothendieck’s duality conjecture. It generalizes the perfectness of the Cassels–Tate pairing in the finite base field case. The proof uses the local duality mentioned above, Artin–Milne’s global finite flat duality, the nondegeneracy of the height pairing and finiteness of crystalline cohomology. All these ingredients are organized under the formalism of the rational étale site developed earlier.

Sign in / Sign up

Export Citation Format

Share Document