ترغب بنشر مسار تعليمي؟ اضغط هنا

Descent for semiorthogonal decompositions

158   0   0.0 ( 0 )
 نشر من قبل Elden Elmanto
 تاريخ النشر 2019
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

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.

قيم البحث

اقرأ أيضاً

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 d ecomposes 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.
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 absolu tely 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.
157 - Lex E. Renner 2008
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 result s 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.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا