Publications arising from SPP 1786-related activities

Mixed Hodge structures in homotopy theory

D.Chataur, J.Cirici, Rational homotopy of complex projective varieties with normal isolated singularities. arXiv:1503.05347 [math.AT] 

J. Cirici, F. Guillén, Homotopy theory of mixed Hodge complexes. Tohoku Mathematical Journal (to appear).

J. Cirici, Cofibrant models of diagrams: mixed Hodge structures in rational homotopy.  Transactions of the American Mathematical Society 367 (2015), no.8, 5935--5970.

Motivic stack inertia for modui spaces of curves, variation of periods and multiple zeta values in genus 0 and 1.

Benjamin Collas, Sylvain Maugeais, On Galois action on stack inertia of moduli spaces of curves. arXiv:1412.4644.

Motivic iterated integrals and integral points

Ishai Dan-Cohen, and Stefan Wewers, Mixed Tate motives and the unit equation. International Mathematics Research Notices, Issue 17, 2016

Ishai Dan-Cohen, Explicit motivic Chabauty-Kim theory III: towards the polylogarithmic quotient over general number fields. 28 pages. arxiv.org/abs/1510.01362

Motives with modulus

H. Esnault, M. Kerz and O. Wittenberg, A restriction isomorphism for cycles of relative dimension zero. preprint, 2015, http://arxiv.org/abs/1503.08187

M. Kerz, Transfinite limits in topos theory, 2015, http://arxiv.org/abs/1502.01923

F.Binda and S.Saito, Relative Cycles with moduli and regulator maps, arXiv:1412.0385[math.AG], submitted. 50 pages.

F.Binda, J.Cao, W.Kai, R.Sugiyama, Torsion and divisibility for reciprocity sheaves and 0-cycles with modulus, arXiv:1503.02161[math.AG], submitted. 28 pages.

F.Binda and A.Krishna, Zero cycles with modulus and zero-cycles on singular varieties, preprint, November 2015, 47 pages

F.Binda Torsion zero-cycles with modulus on affine varieties, preprint, October 2015, 11 pages.

F.Binda A cycle class map for 0-cycles with modulus to higher relative K-groups, preprint, April 2014, 32 pages.

Characterizations and uniqueness of the stable motivic homotopy category

J. Hornbostel, M. Wendt, Chow-Witt rings of classifying spaces for symplectic and special linear groups, arxiv.org/abs/1703.05362

Applications of motivic methods to differential forms and birational geometry

Annette Huber, Stefan Kebekus, Shane Kelly, Differential forms in positive characteristic avoiding resolution of singularities. arxiv.org/abs/1407.5786

Hélène Esnault, A. Shiho, Chern classes of crystals, preprint 2015. arXiv:1511.06874

Hélène Esnault, Michael Harris, Chern classes of automorphic vector bundles, preprint 2017. arXiv:1701.09073

Ofer Gabber, Shane Kelly, Points in algebraic geometry. J. Pure Appl. Algebra 219 (2015), no. 10, 4667–4680.

Shane Kelly, Voevodsky motives and ldh descent To appear Astérisque (accepted Feb 2017).

Annette Huber, Stefan Kebekus, Shane Kelly, Differential forms in positive characteristic avoiding resolution of singularities To appear Bull. de la SMF arXiv:1407.5786

Shane Kelly, Un isomorphisme de Suslin. arXiv:1407.5772

Shane Kelly, Shuji Saito, Weight homology of motives To appear Int.Math.Res.Not. arXiv:1411.5831

Shane Kelly, Some observations about motivic tensor triangulated geometry over a finite field, arXiv:1608.02913

Jens Niklas Eberhardt, Shane Kelly, Mixed Motives and Geometric Representation Theory in Equal Characteristic, arXiv:1609.05956

Motivic filtrations over Dedekind domains

Alexey Ananyevskiy, Marc Levine and Ivan Panin, Witt sheaves and the $\eta$-inverted sphere spectrum preprint (April 2015) arXiv:1504.04860 [math.AT]

Marc Levine, The intrinsic stable normal cone, arXiv:1703.03056

Marc Levine, Toward an enumerative geometry with quadratic forms, arXiv:1703.03049

Marc Levine, Yaping Yang, Gufang Zhao, Algebraic elliptic cohomology and flops II: SL-cobordism arXiv:1610.00396

Andre Chatzistamatiou, Marc Levine, Torsion orders of complete intersections, arXiv:1605.01913

Marc Levine, Intersection theory in algebraic cobordism. J. Pure Appl. Algebra 221 (2017), no. 7, 1645–1690.

Marc Levine, An overview of motivic homotopy theory. Acta Math. Vietnam. 41 (2016), no. 3, 379–407.

Hélène Esnault, T. Abe, A Lefschetz theorem for overconvergent isocrystals with Frobenius structure, preprint 2016 arXiv:1607.07112

Oliver Röndigs, Markus Spitzweck, Paul Arne Østvær, Cellularity of hermitian K-theory and Witt theory arXiv:1603.05139, Proceedings of the International Colloquium at TIFR held in January, Chief Editor Ravi A. Rao, 2016.

Oliver Röndigs, Markus Spitzweck, Paul Arne Østvær, The motivic Hopf map solves the homotopy limit problem for K-theory, arXiv:1701.06144.

Oliver Röndigs, Markus Spitzweck, Paul Arne Østvær, The first stable homotopy groups of motivic spheres, arXiv:1604.00365.

J.D. Christensen, M. Frankland, Higher Toda brackets and the Adams spectral sequence in trianglated categories, to appear, Algebr. Geom. Topol., 2017 https://arxiv:1510.09216

H.J. Baues, M. Frankland, Eilenberg-MacLane mapping algebras and higher distributivity up to homotopy, arXiv:1703.07512.

M. Frankland, A user's guide: Completed power operations for Morava E-theory, expository article at mathusersguides.org, 2016.

M. Frankland, M. Spitzweck, A possible approach to the Hopkins-Morel isomorphism over general base schemes, Work in progress.

The Summand BtmfP of MU<6>

Gerd Laures, Characteristic classes in TMF of level Γ1(3), Trans. Amer. Math. Soc. 368 (2016), no. 10, 7339--7357.

Gerd Laures and Martin Olbermann, TMF0(3)-characteristic classes for string bundles, Math. Z. 282 (2016), no. 1-2, 511--533.

Expansion principles for topological automorphic forms

Hanno von Bodecker and Sebastian Thyssen, On p-local Topological Automorphic Forms for U(1,1;Z[i]). arXiv:1609.08869, 2016

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New examples of logarithmic ring spectra

Irina Bobkova, Ayelet Lindenstrauss, Kate Poirier, Birgit Richter, Inna Zakharevich, On the higher topological Hochschild homology of $\mathbb{F}_p$ and commutative $\mathbb{F}_p$-group algebras, in: Women in Topology: Collaborations in Homotopy Theory. Contemporary Mathematics 641, AMS, 2015, 97--122.

Birgit Richter, On the homology and homotopy of commutative shuffle algebras, Israel Journal of Mathematics 209 (2), 2015, 651--682.

John Rognes, Steffen Sagave, and Christian Schlichtkrull, Localization sequences for logarithmic topological Hochschild homology,Mathematische Annalen, 363 (2015), no. 3, 1349–1398 http://dx.doi.org/10.1007/s00208-015-1202-3

Bjørn Ian Dundas, Ayelet Lindenstrauss, Birgit Richter, On higher topological Hochschild homology of rings of integers. arXiv:1502.02504

Operadic structures in motivic homotopy theory

Kyle Ormsby, Oliver Röndigs, Paul Arne Østvær, Vanishing in stable motivic homotopy sheaves arXiv:1704.04744

Oliver Röndigs, On the η-inverted sphere. arXiv:1602.08798

Oliver Röndigs, Markus Spitzweck, Paul Arne Østvær, The first stable homotopy groups of motivic spheres, arXiv:1604.00365.

G. Biedermann, G. Raptis, M. Stelzer, The realization space of an unstable coalgebra, to appear, Asterisque, arxiv:1409.0410.

M. Stelzer, Simplicial coalgebras over a Prüfer domain and homotopy theory. Preprint

Global equivariant homotopy theory

Markus Hausmann, Symmetric spectra model global homotopy theory of finite groups, arXiv:1509.09270

Markus Hausmann, Dominik Ostermayr, Filtrations of global equivariant K-theory, arXiv:1510.04011

Markus Hausmann, Symmetric products and subgroup lattices, arXiv:1607.07559

Stefan Schwede, Equivariant properties of symmetric products, Journal of the American Mathematical Society 30 (2017), 673-711.

Odd primary equivariant rigidity and equivariant derivators

Irakli Patchkoria, Rigidity in Equivariant Stable Homotopy Theory, Algebr. Geom. Topol. 16 (2016), no. 4, 2159–2227.

Irakli Patchkoria, Constanze Roitzheim, Rigidity and exotic models for $v_1$-local $G$-equivariant stable homotopy theory, arXiv:1705.03855

Oriented cohomology theories and equivariant motives

A. Neshitov, V. Petrov, N. Semenov, K. Zainoulline, Motivic decompositions of twisted flag varieties and representations of Hecke-type algebras, arxiv.org/abs/1505.07083

V. Petrov, N. Semenov, Rost motives, affine varieties, and classifying spaces, arxiv.org/abs/1506.07788