Motivic invariants of birational maps
We construct invariants of birational maps with values in the Kontsevich--Tschinkel group
and in the truncated Grothendieck groups of varieties. These invariants are morphisms of …
and in the truncated Grothendieck groups of varieties. These invariants are morphisms of …
[PDF][PDF] Cycle class maps and birational invariants
B Hassett, Y Tschinkel - arXiv preprint arXiv:1908.00406, 2019 - arxiv.org
arXiv:1908.00406v1 [math.AG] 1 Aug 2019 Page 1 arXiv:1908.00406v1 [math.AG] 1 Aug 2019
CYCLE CLASS MAPS AND BIRATIONAL INVARIANTS BRENDAN HASSETT AND YURI …
CYCLE CLASS MAPS AND BIRATIONAL INVARIANTS BRENDAN HASSETT AND YURI …
Curve classes on conic bundle threefolds and applications to rationality
We undertake a study of conic bundle threefolds $\pi\colon X\to W $ over geometrically
rational surfaces whose associated discriminant covers $\tilde {\Delta}\to\Delta\subset W …
rational surfaces whose associated discriminant covers $\tilde {\Delta}\to\Delta\subset W …
Arithmetic occult period maps
J Achter - arXiv preprint arXiv:1904.04288, 2019 - arxiv.org
Several natural complex configuration spaces admit surprising uniformizations as arithmetic
ball quotients, by identifying each parametrized object with the periods of some auxiliary …
ball quotients, by identifying each parametrized object with the periods of some auxiliary …
Generic cycles, Lefschetz representations, and the generalized Hodge and Bloch conjectures for abelian varieties
C Vial - arXiv preprint arXiv:1803.00857, 2018 - arxiv.org
We prove Bloch's conjecture for correspondences on powers of complex abelian varieties,
that are" generically defined". As an application we establish vanishing results for (skew-) …
that are" generically defined". As an application we establish vanishing results for (skew-) …
Derived equivalent threefolds, algebraic representatives, and the coniveau filtration
A conjecture of Orlov predicts that derived equivalent smooth projective varieties over a field
have isomorphic Chow motives. The conjecture is known for curves, and was recently …
have isomorphic Chow motives. The conjecture is known for curves, and was recently …
[HTML][HTML] Motivic periods and Grothendieck arithmetic invariants
We construct a period regulator for motivic cohomology of an algebraic scheme over a
subfield of the complex numbers. For the field of algebraic numbers we formulate a period …
subfield of the complex numbers. For the field of algebraic numbers we formulate a period …
Normal functions for algebraically trivial cycles are algebraic for arithmetic reasons
For families of smooth complex projective varieties, we show that normal functions arising
from algebraically trivial cycle classes are algebraic and defined over the field of definition of …
from algebraically trivial cycle classes are algebraic and defined over the field of definition of …
The Walker Abel–Jacobi map descends
For a complex projective manifold, Walker has defined a regular homomorphism lifting
Griffiths' Abel–Jacobi map on algebraically trivial cycle classes to a complex abelian variety …
Griffiths' Abel–Jacobi map on algebraically trivial cycle classes to a complex abelian variety …
Motivic periods and Grothendieck arithmetic invariants
A Fabrizio, L Barbieri-Viale, A Bertapelle… - ADVANCES IN …, 2020 - research.unipd.it
We construct a period regulator for motivic cohomology of an algebraic scheme over a
subfield of the complex numbers. For the field of algebraic numbers we formulate a period …
subfield of the complex numbers. For the field of algebraic numbers we formulate a period …