The central objects in the book are Lagrangian submanifolds and their invariants, such as
Floer homology and its multiplicative structures, which together constitute the Fukaya …

arXiv:math/0601185v5 [math.KT] 19 Jun 2006 Page 1 arXiv:math/0601185v5 [math.KT] 19 Jun
2006 ON DIFFERENTIAL GRADED CATEGORIES BERNHARD KELLER Abstract. Differential …

We define the spectrum of a tensor triangulated category as the set of so-called prime ideals,
endowed with a suitable topology. In this very generality, the spectrum is the universal space …

In this paper we introduce a new notion of weight structure (w) for a triangulated category C;
this notion is an important natural counterpart of the notion of t-structure. It allows extending …

This book combines foundational constructions in the theory of motives and results relating
motivic cohomology to more explicit constructions. Prerequisite for understanding the work is …

We categorify Lusztig's U˙—a version of the quantized enveloping algebra Uq (sl2). Using a
graphical calculus a 2-category U˙ is constructed whose split Grothendieck ring is …

We define a theory of étale motives over a noetherian scheme. This provides a system of
categories of complexes of motivic sheaves with integral coefficients which is closed under …

In this article, we construct étale realization functors defined on the categories DAét (X, Λ) of
étale motives (without transfers) over a scheme X. Our construction is natural and relies on a …

Katzarkov has proposed a generalization of Kontsevich's mirror symmetry conjecture,
covering some varieties of general type. We prove a version of this conjecture in the simplest …

We present a simplified and more intuitive proof of a theorem of Peng and Xiao, which
constructs a Lie algebra from any 2-periodic triangulated k-category (satisfying some …