On the Brauer group of Enriques surfaces

Arnaud Beauville

Description

On the Brauer group of Enriques surfaces Arnaud Beauville Universite de Nice Madrid, December 2009 Arnaud Beauville On the Brauer group of Enriques surfaces

• rational varieties


• artin-mumford


• variety over


• enriques surfaces


• severi-brauer fibrations


• coherent sheaves


• universite de nice

Sujets

• Beauville
• Rational variety
• Enriques surface
• Coherent sheaf
• Universidad de Niza Sophia Antipolis

Informations

• Publié par: pefav
• Nombre de lectures: 10
• Langue: English

Extrait

On the Brauer group of Enriques surfaces
Arnaud Beauville
Universite de Nice
Madrid, December 2009
Arnaud Beauville On the Brauer group of Enriques surfacesBr(K ) important in number theory and algebra.
Br(S) birational invariant { detects non-rational varieties
(Artin-Mumford).
nBr(S) classi es Severi-Brauer brations (= P -bundles) over S
2Br(S) an abelian category Coh (S) of \-twisted
coherent sheaves".
For S over a number eld, Br(S) provides the Brauer-Manin
obstruction to the existence of rational points.
S smooth projective variety overC
2 2 Br(S) := H (S;G ) H (S;O )=m torset hol
Why is it interesting?
The Brauer group
Arnaud Beauville On the Brauer group of Enriques surfacesBr(K ) important in number theory and algebra.
Br(S) birational invariant { detects non-rational varieties
(Artin-Mumford).
nBr(S) classi es Severi-Brauer brations (= P -bundles) over S
2Br(S) an abelian category Coh (S) of \-twisted
coherent sheaves".
For S over a number eld, Br(S) provides the Brauer-Manin
obstruction to the existence of rational points.
2 2 Br(S) := H (S;G ) H (S;O )=m torset hol
Why is it interesting?
The Brauer group
S smooth projective variety overC
Arnaud Beauville On the Brauer group of Enriques surfacesBr(K ) important in number theory and algebra.
Br(S) birational invariant { detects non-rational varieties
(Artin-Mumford).
nBr(S) classi es Severi-Brauer brations (= P -bundles) over S
2Br(S) an abelian category Coh (S) of \-twisted
coherent sheaves".
For S over a number eld, Br(S) provides the Brauer-Manin
obstruction to the existence of rational points.
2 H (S;O )= torshol
Why is it interesting?
The Brauer group
S smooth projective variety overC
2Br(S) := H (S;G )met
Arnaud Beauville On the Brauer group of Enriques surfacesBr(K ) important in number theory and algebra.
Br(S) birational invariant { detects non-rational varieties
(Artin-Mumford).
nBr(S) classi es Severi-Brauer brations (= P -bundles) over S
2Br(S) an abelian category Coh (S) of \-twisted
coherent sheaves".
For S over a number eld, Br(S) provides the Brauer-Manin
obstruction to the existence of rational points.
Why is it interesting?
The Brauer group
S smooth projective variety overC
2 2 Br(S) := H (S;G ) H (S;O )=m torset hol
Arnaud Beauville On the Brauer group of Enriques surfacesBr(K ) important in number theory and algebra.
Br(S) birational invariant { detects non-rational varieties
(Artin-Mumford).
nBr(S) classi es Severi-Brauer brations (= P -bundles) over S
2Br(S) an abelian category Coh (S) of \-twisted
coherent sheaves".
For S over a number eld, Br(S) provides the Brauer-Manin
obstruction to the existence of rational points.
The Brauer group
S smooth projective variety overC
2 2 Br(S) := H (S;G ) H (S;O )=m torset hol
Why is it interesting?
Arnaud Beauville On the Brauer group of Enriques surfacesBr(S) birational invariant { detects non-rational varieties
(Artin-Mumford).
nBr(S) classi es Severi-Brauer brations (= P -bundles) over S
2Br(S) an abelian category Coh (S) of \-twisted
coherent sheaves".
For S over a number eld, Br(S) provides the Brauer-Manin
obstruction to the existence of rational points.
The Brauer group
S smooth projective variety overC
2 2 Br(S) := H (S;G ) H (S;O )=m torset hol
Why is it interesting?
Br(K ) important in number theory and algebra.
Arnaud Beauville On the Brauer group of Enriques surfacesnBr(S) classi es Severi-Brauer brations (= P -bundles) over S
2Br(S) an abelian category Coh (S) of \-twisted
coherent sheaves".
For S over a number eld, Br(S) provides the Brauer-Manin
obstruction to the existence of rational points.
The Brauer group
S smooth projective variety overC
2 2 Br(S) := H (S;G ) H (S;O )=m torset hol
Why is it interesting?
Br(K ) important in number theory and algebra.
Br(S) birational invariant { detects non-rational varieties
(Artin-Mumford).
Arnaud Beauville On the Brauer group of Enriques surfaces2Br(S) an abelian category Coh (S) of \-twisted
coherent sheaves".
For S over a number eld, Br(S) provides the Brauer-Manin
obstruction to the existence of rational points.
The Brauer group
S smooth projective variety overC
2 2 Br(S) := H (S;G ) H (S;O )=m torset hol
Why is it interesting?
Br(K ) important in number theory and algebra.
Br(S) birational invariant { detects non-rational varieties
(Artin-Mumford).
nBr(S) classi es Severi-Brauer brations (= P -bundles) over S
Arnaud Beauville On the Brauer group of Enriques surfacesFor S over a number eld, Br(S) provides the Brauer-Manin
obstruction to the existence of rational points.
The Brauer group
S smooth projective variety overC
2 2 Br(S) := H (S;G ) H (S;O )=m torset hol
Why is it interesting?
Br(K ) important in number theory and algebra.
Br(S) birational invariant { detects non-rational varieties
(Artin-Mumford).
nBr(S) classi es Severi-Brauer brations (= P -bundles) over S
2Br(S) an abelian category Coh (S) of \-twisted
coherent sheaves".
Arnaud Beauville On the Brauer group of Enriques surfaces