On the cycle class map for zero-cycles over local fields

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On the cycle class map for zero-cycles over local fields
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The Chow group of zero-cycles of a smooth and projective variety defined over a field k is an invariant of an arithmetic and geometric nature which is well understood only when k is a finite field (by higher-dimensional class field theory). In this talk, we will discuss the case of local and strictly local fields. We prove in particular the injectivity of the cycle class map to integral l-adic cohomology for a large class of surfaces with positive geometric genus over p-adic fields. The same statement holds for semistable K3 surfaces over C((t)), but does not hold in general for surfaces over C((t)) or over the maximal unramified extension of a p-adic field. This is a joint work with Hélène Esnault.
Meeting/Interview Mathematics Grothendieck topology Resultant
Group action Musical ensemble Existential quantification State of matter Multiplication sign Materialization (paranormal) 1 (number) Weight Group representation Sign (mathematics) Many-sorted logic Descriptive statistics Area Perturbation theory Substitute good Dean number Arithmetic mean Graph coloring Hausdorff dimension Right angle Cycle (graph theory) Resultant Fundamental theorem of algebra Directed graph Finitismus Observational study Variety (linguistics) Student's t-test Rule of inference Event horizon Theory Number Goodness of fit Lecture/Conference Average Energy level Renewal theory Units of measurement Series (mathematics) Forcing (mathematics) Algebraic structure Division (mathematics) Incidence algebra Local Group Field extension Voting Thermal radiation Universe (mathematics) Family
Point (geometry) Greatest element Link (knot theory) Euler angles Multiplication sign Connectivity (graph theory) Student's t-test Parameter (computer programming) Mereology Rule of inference Grothendieck topology Strategy game Many-sorted logic Thermodynamisches System Root Lecture/Conference Stress (mechanics) 9 (number) Physical system Condition number Area Spacetime Product (category theory) Generating set of a group Surface Forcing (mathematics) Moment (mathematics) Physical law Volume (thermodynamics) Incidence algebra Contingency table Variable (mathematics) Sequence Field extension Universe (mathematics) Iteration Right angle Cycle (graph theory) Family Local ring Fundamental theorem of algebra Resultant Annihilator (ring theory) Directed graph
Point (geometry) Variety (linguistics) Image resolution 1 (number) Insertion loss Routing Event horizon Rule of inference Grothendieck topology Frequency Latent heat Fisher information Strategy game Thermodynamisches System Lecture/Conference Well-formed formula Negative number Energy level Stochastic kernel estimation Subtraction Units of measurement Condition number Stability theory Flux Area Addition Series (mathematics) Generating set of a group Forcing (mathematics) Topological vector space Local Group Arithmetic mean Exterior algebra Logic Universe (mathematics) Object (grammar) Uniform space Arithmetic progression Resultant Local ring
Trigonometry Sheaf (mathematics) Mereology Weight Rule of inference Frequency Centralizer and normalizer Coefficient of determination Goodness of fit Thermodynamisches System Lecture/Conference Selectivity (electronic) Units of measurement Area Series (mathematics) Spacetime Process (computing) Theory of relativity Coalition Product (category theory) Moment (mathematics) Incidence algebra Bilinear form Local Group Voting Lattice (order) Arithmetic progression Resultant
Euler angles Multiplication sign Incidence algebra Limit (category theory) Variable (mathematics) Mereology Rule of inference Local Group Grothendieck topology Field extension Lecture/Conference Thermal radiation Hausdorff dimension Energy level Cycle (graph theory) Associative property Glass float Resultant Stability theory
Observational study State of matter Variety (linguistics) Multiplication sign Insertion loss Rule of inference Grothendieck topology Number Goodness of fit Thermodynamisches System Lecture/Conference Operator (mathematics) Fiber (mathematics) Area Multiplication Generating set of a group Surface Moment (mathematics) Physicalism Mathematical model Bilinear form Commutator Right angle Family Resultant
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