Publications and preprints arising from SPP 1786-related activities

### Mixed Hodge structures in homotopy theory

J. Cirici, D. Egas Santander, M. Livernet and S. Whitehouse, Derived A-infinity algebras and their homotopies. Topology and its Applications (special issue) to appear (also available at http://arxiv.org/abs/1609.08077).

D.Chataur, J.Cirici, Rational homotopy of complex projective varieties with normal isolated singularities. Forum Mathematicum 29 (2017), no.1, 41--57

J. Cirici, F. Guillén, Homotopy theory of mixed Hodge complexes.Tohoku Mathematical Journal 68 (2016), no.3, 349--375.

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

U. Buijs and F. Cantero and J. Cirici, Weight decompositions of Thom spaces of vector bundles in rational homotopy theory. arXiv:1610.02917 [math.AT] 2017

Cirici and G. Horel, Mixed Hodge structures and formality of symmetric monoidal functors. arXiv:1703.06816 [math.AT] 2017

J. Cirici and A. Roig, Sullivan minimal models of operad algebras. arXiv:1612.03862 [math.AT] 2016

Chataur and J. Cirici, Mixed Hodge structures on the intersection homotopy type of complex varieties with isolated singularities. arXiv:1603.09125 [math.AT] 2016

### 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

Tom Bachmann, Motivic and Real Etale Stable Homotopy Theory. https://arxiv.org/abs/1608.08855.

Tom Bachmann, The Generalized Slices of Hermitian K-Theory https://arxiv.org/abs/1610.01346 to appear Jour. of Topology.

Tom Bachmann, Some Remarks on Units in Grothendieck-Witt Rings https://arxiv.org/abs/1612.04728

Tom Bachmann and Alexander Vishik, Motivic equivalence of affine quadrics. https://arxiv.org/abs/1707.08087.

Tom Bachmann and Jean Fasel, On the effectivity of spectra representing motivic cohomology theories. https://arxiv.org/abs/1710.00594.

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

Wataru Kai and H. Miyazaki, Suslin's moving lemma with modulus. Annals of K-theory 3 (1) 2018, 55-70.

Wataru Kai and Ryomei Iwasa, Chern classes with modulus. arXiv:1611.07882 [math.KT].

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

Shane Kelly, Voevodsky motives and ldh descent. Astérisque 391 (2017).

Annette Huber, Differential forms in algebraic geometry -- a new perspective in the singular case. Portugaliae Mathematica 73 (2016), no. 4, 337--367.

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

Annette Huber, Shane Kelly, Differential forms in positive characteristic II: cdh-descent via functorial Riemann-Zariski spaces . Preprint 2017, arXiv:1706.05244

Annette Huber, Stefan Kebekus, Shane Kelly, Differential forms in positive characteristic avoiding resolution of singularities. To appear Bull. de la SMF.arxiv.org/abs/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

### The Summand $BtmfP$ of $MU\langle 6\rangle$

Laures, G. and Olbermann, M..Cannibalistic classes of string bundles. Manuscripta math. (2017). doi.org/10.1007/s00229-017-0978-8.

Laures, G. and Schuster, B.  Towards a splitting of the K(2)-local string bordism spectrum, arXiv:1710.03427.

Gerd Laures, Characteristic classes in $TMF$ of level $\Gamma_1(3)$, Trans. Amer. Math. Soc. 368 (2016), no. 10, 7339--7357.

Gerd Laures and Martin Olbermann, $TMF_0(3)$-characteristic classes for string bundles, Math. Z. 282 (2016), no. 1-2, 511--533.

### Expansion principles for topological automorphic forms

Hanno von Bodecker, Sebastian Thyssen. Topological Automorphic Forms via Curves  arXiv:1705.02134.

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

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### 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.

### Chromatic derived algebraic geometry and equivariant homotopy theory

John Greenlees and Lennart Meier. Gorenstein duality for Real spectra Algebraic & Geometric Topology 17 (2017), 3547-3619

Mike Hill and Lennart Meier. The C2-spectrum Tmf1(3) and its invertible modules Algebraic & Geometric Topology 17 (2017) 1953-2011.

Lennart Meier. Decomposition results for rings of modular forms. arXiv:1710.03461

Rosona Eldred, Gijs Heuts, Akhil Mathew and Lennart Meier. Monadicity of the Bousfield-Kuhn functor. arXiv:1707.05986

Lennart Meier. (Topological) modular forms with level structures: decompositions and duality. arXiv:1609.09264

Ben Antieau and Lennart Meier. The Brauer group of the moduli stack of elliptic curves. arXiv:1608.00851

### Beyond spin bordism

Akhil Mathew, Niko Naumann and Justin Noel, Nilpotence and descent in equivariant stable homotopy theory. Advances in Mathematics, vol.\ 305, pp.\ 994-1084, January 2017. arXiv: http://arxiv.org/abs/1507.06867

### Preprints

Akhil Mathew, Niko Naumann and Justin Noel, Derived induction and restriction theory. arXiv: http://arxiv.org/abs/1507.06869

Tobias Barthel, Markus Hausmann, Niko Naumann and Justin Noel, Thomas Nikolaus, and Nathaniel Stapleton The Balmer spectrum of the equivariant homotopy category of a finite abelian group. arXiv: https://arxiv.org/abs/1709.04828.

Dustin Clausen, Akhil Mathew, Niko Naumann and Justin Noel, Descent in algebraic $K$-theory and a conjecture of Ausoni-Rognes. arXiv: https://arxiv.org/abs/1606.03328.

### New examples of logarithmic ring spectra

Birgit Richter, Brooke Shipley, An algebraic model for commutative H$\mathbb{Z}$-algebras, Algebr. Geom. Topol. 17 (2017), no. 4, 2013--2038.

Birgit Richter, Commutative ring spectra arXiv:1710.02328

Gemma Halliwell, Eva Höning, Ayelet Lindenstrauss, Birgit Richter, Inna Zakharevich, Relative Loday constructions and applications to higher THH-calculations, accepted for publication in Topology and its Applications. arXiv:1609.02397

Bjørn Ian Dundas, Ayelet Lindenstrauss, Birgit Richter, Towards an understanding of ramified extensions of structured ring spectra.arXiv:1604.05857

Bjørn Ian Dundas, Ayelet Lindenstrauss, Birgit Richter, On higher topological Hochschild homology of rings of integers, accepted for publication in Mathematical Research Letters. arXiv:1502.02504.

John Rognes, Steffen Sagave, and Christian Schlichtkrull, Logarithmic topological Hochschild homology of topological K-theory spectra, accepted for publication in Journal of the European Mathematical Society (JEMS). arXiv:1410.2170.

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

Stefan Schwede, Orbispaces, orthogonal spaces, and the universal compact Lie group, arXiv:1711.06019

Christian Wimmer, Rational global homotopy theory and geometric fixed points. PhD thesis, Universität Bonn, 2017

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

## Guests and visitors

Matthias Wendt (visiting Jens Hornbostel, Wuppertal, October/November 2017)

### Preprints and publications

Jens Hornbostel, Matthias Wendt. Chow--Witt rings of classifying spaces for symplectic and special linear groups, arXiv:1703.05362.

Matthias Wendt. On stably trivial spin torsors over low-dimensional schemes, arXiv:1704.07768.

Drew Heard (visiting Birgit Richter, Hamburg, 01.10.2016--30.09.2017)

### Preprints and publications

Drew Heard. On equivariant and motivic slices. 2017. In preparation.

Drew Heard and Achim Krause. Vanishing lines for modules over the motivic Steenrod algebra., 2017. arXiv:1702.03683.

Drew Heard. The homotopy limit problem and the cellular Picard group of Hermitian K-theory. 2017. arXiv:1705.02810.

Tobias Barthel and Drew Heard. Algebraic chromatic homotopy theory. 2017. arXiv:1708.09261.

Tobias Barthel, Natalia Castellana, Drew Heard, and Gabriel Valenzuela. Stratification and duality for homotopical groups. 2017. arXiv:1711.03491.