6 papers
Compact approximation and descent for algebraic stacks
Jack Hall, Alicia Lamarche, Pat Lank +1
This work focuses on approximation and generation for the derived category of complexes with quasi-coherent cohomology on algebraic stacks. Our methods establish that approximation…
On decompositions for Fano schemes of intersections of two quadrics
Pieter Belmans, Jishnu Bose, Sarah Frei +6
We propose conjectural semiorthogonal decompositions for Fano schemes of linear subspaces on intersections of two quadrics, in terms of symmetric powers of the associated hyperelli…
Global generation of test ideals in mixed characteristic and applications
Christopher Hacon, Alicia Lamarche, Karl Schwede
Suppose that is an integral scheme (quasi-)projective over a complete local ring of mixed characteristic. Using ideas of Takamatsu-Yoshikawa and Bhatt-Ma-et. al, we define a no…
Consequences of the existence of exceptional collections in arithmetic and rationality
Matthew R. Ballard, Alexander Duncan, Alicia Lamarche +1
A well-known conjecture of Orlov asks whether the existence of a full exceptional collection implies rationality of the underlying variety. We prove this conjecture for arithmetic…
A transcendental Brauer-Manin obstruction to weak approximation on a Calabi-Yau threefold
Sachi Hashimoto, Katrina Honigs, Alicia Lamarche +1
In this paper we investigate the -rational points of a class of simply connected Calabi-Yau threefolds, which were originally studied by Hosono and Takagi in the contex…
Separable algebras and coflasque resolutions
Matthew R. Ballard, Alexander Duncan, Alicia Lamarche +1
Over a non-closed field, it is a common strategy to use separable algebras as invariants to distinguish algebraic and geometric objects. The most famous example is the deep connect…