Daniel Schäppi
YOU?
Author Swipe
View article: A counterexample to the Hermite ring conjecture
A counterexample to the Hermite ring conjecture Open
We show that there exists a stably free module over a polynomial ring which is not extended from the ground ring. This provides a counterexample to the Hermite ring conjecture.
View article: Symplectic K-theory and a problem of Murthy
Symplectic K-theory and a problem of Murthy Open
We compute low-dimensional K-groups of certain rings associated with the study of the Hermite ring conjecture. This includes a monoid ring whose low-dimensional K-groups were recently computed by Krishna and Sarwar in the case where the ba…
View article: Flat functors in higher topos theory
Flat functors in higher topos theory Open
For a small $n$-category $\mathscr{C}$ and an $n$-topos $\mathscr{X}$, we study necessary and sufficient conditions for a functor $f \colon \mathscr{C} \to \mathscr{X}$ to determine a geometric morphism from $\mathscr{X}$ to the $n$-topos …
View article: Formal Laurent series rings and the Hermite ring conjecture
Formal Laurent series rings and the Hermite ring conjecture Open
We study the question if projective modules over formal Laurent series rings are extended. We relate this question to the Bass-Quillen conjecture for commutative regular local rings and to the Hermite ring conjecture for all commutative lo…
View article: Flat replacements of homology theories
Flat replacements of homology theories Open
To a homology theory one can associate an additive site and a new homological functor with values in the category of additive sheaves on that site. If this category of sheaves can be shown to be equivalent to a category of comodules of a H…
View article: Graded-Tannakian categories of motives
Graded-Tannakian categories of motives Open
Given a rigid tensor-triangulated category and a vector space valued homological functor for which the Künneth isomorphism holds, we construct a universal graded-Tannakian category through which the given homological functor factors. We us…
View article: The formal theory of Tannaka duality
The formal theory of Tannaka duality Open
A Tannakian category is an abelian tensor category equipped with a fiber functor and additional structures which ensure that it is equivalent to the category of representations of some affine groupoid scheme acting on the spectrum of a fie…
View article: Uniqueness of fiber functors and universal Tannakian categories
Uniqueness of fiber functors and universal Tannakian categories Open
The principal aim of this note is to give an elementary proof of the fact that any two fiber functors of a Tannakian category are locally isomorphic. This builds on an idea of Deligne concerning scalar extensions of Tannakian categories an…
View article: When coproducts are biproducts
When coproducts are biproducts Open
Among monoidal categories with finite coproducts preserved by tensoring on the left, we characterise those with finite biproducts as being precisely those in which the initial object and the coproduct of the unit with itself admit right du…