Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userDescent for semiorthogonal decompositions
158
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We prove descent theorems for semiorthogonal decompositions using techniques from derived algebraic geometry. Our methods allow us to capture more general filtrations of derived categories and even marked filtrations, where one descends not only admissible subcategories but also preferred objects.
rate research
Read More
We study the birational properties of geometrically rational surfaces from a derived categorical point of view. In particular, we give a criterion for the rationality of a del Pezzo surface over an arbitrary field, namely, that its derived category decomposes into zero-dimensional components. For del Pezzo surfaces of degree at least 5, we construct explicit semiorthogonal decompositions by subcategories of modules over semisimple algebras arising as endomorphism algebras of vector bundles and we show how to retrieve information about the index of the surface from Brauer classes and Chern classes associated to these vector bundles.
We study the derived category of coherent sheaves on vario
A theorem of N. Katz cite{Ka} p.45, states that an irreducible differential operator $L$ over a suitable differential field $k$, which has an isotypical decomposition over the algebraic closure of $k$, is a tensor product $L=Motimes_k N$ of an absolutely irreducible operator $M$ over $k$ and an irreducible operator $N$ over $k$ having a finite differential Galois group. Using the existence of the tensor decomposition $L=Motimes N$, an algorithm is given in cite{C-W}, which computes an absolutely irreducible factor $F$ of $L$ over a finite extension of $k$. Here, an algorithmic approach to finding $M$ and $N$ is given, based on the knowledge of $F$. This involves a subtle descent problem for differential operators which can be solved for explicit differential fields $k$ which are $C_1$-fields.
Let $(W,S)$ be a finite Weyl group and let $win W$. It is widely appreciated that the descent set D(w)={sin S | l(ws)<l(w)} determines a very large and important chapter in the study of Coxeter groups. In this paper we generalize some of those results to the situation of the Bruhat poset $W^J$ where $Jsubseteq S$. Our main results here include the identification of a certain subset $S^Jsubseteq W^J$ that convincingly plays the role of $Ssubseteq W$, at least from the point of view of descent sets and related geometry. The point here is to use this resulting {em descent system} $(W^J,S^J)$ to explicitly encode some of the geometry and combinatorics that is intrinsic to the poset $W^J$. In particular, we arrive at the notion of an {em augmented poset}, and we identify the {em combinatorially smooth} subsets $Jsubseteq S$ that have special geometric significance in terms of a certain corresponding torus embedding $X(J)$. The theory of $mathscr{J}$-irreducible monoids provides an essential tool in arriving at our main results.
We give necessary and sufficient conditions for a cdh sheaf to satisfy Milnor excision, following ideas of Bhatt and Mathew. Along the way, we show that the cdh infinity-topos of a quasi-compact quasi-separated scheme of finite valuative dimension is hypercomplete, extending a theorem of Voevodsky to nonnoetherian schemes. As an application, we show that if E is a motivic spectrum over a field k which is n-torsion for some n invertible in k, then the cohomology theory on k-schemes defined by E satisfies Milnor excision.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
